Thermoelectric devices and systems

ABSTRACT

The present disclosure provides a thermoelectric element comprising a flexible semiconductor substrate having exposed surfaces with a metal content that is less than about 1% as measured by x-ray photoelectron spectroscopy (XPS) and a figure of merit (ZT) that is at least about 0.25, wherein the flexible semiconductor substrate has a Young&#39;s Modulus that is less than or equal to about 1×10 6  pounds per square inch (psi) at 25° C.

CROSS-REFERENCE

This application claims priority to U.S. Provisional Patent ApplicationNo. 61/970,322, filed Mar. 25, 2014, and U.S. Provisional PatentApplication No. 62/013,468, filed Jun. 17, 2014, each of which isentirely incorporated herein by reference.

BACKGROUND

Over 15 Terawatts of heat is lost to the environment annually around theworld by heat engines that require petroleum as their primary fuelsource. This is because these engines only convert about 30 to 40% ofpetroleum's chemical energy into useful work. Waste heat generation isan unavoidable consequence of the second law of thermodynamics.

The term “thermoelectric effect” encompasses the Seebeck effect, Peltiereffect and Thomson effect. Solid-state cooling and power generationbased on thermoelectric effects typically employ the Seebeck effect orPeltier effect for power generation and heat pumping. The utility ofsuch conventional thermoelectric devices is, however, typically limitedby their low coefficient-of-performance (COP) (for refrigerationapplications) or low efficiency (for power generation applications).

Thermoelectric device performance may be captured by a so-calledthermoelectric figure-of-merit, Z=S²σ/k, where ‘S’ is the Seebeckcoefficient, ‘σ’ is the electrical conductivity, and ‘k’ is thermalconductivity. Z is typically employed as the indicator of the COP andthe efficiency of thermoelectric devices—that is, COP scales with Z. Adimensionless figure-of-merit, ZT, may be employed to quantifythermoelectric device performance, where ‘T’ can be an averagetemperature of the hot and the cold sides of the device.

Applications of conventional semiconductor thermoelectric coolers arerather limited, as a result of a low figure-of-merit, despite manyadvantages that they provide over other refrigeration technologies. Incooling, low efficiency of thermoelectric devices made from conventionalthermoelectric materials with a small figure-of-merit limits theirapplications in providing efficient thermoelectric cooling.

SUMMARY

The present disclosure provides thermoelectric elements, devices andsystems, and methods for forming such elements, devices and systems.

Although there are thermoelectric devices currently available,recognized herein are various limitations associated with suchthermoelectric devices. For example, some thermoelectric devicescurrently available may not be flexible and able to conform to objectsof various shapes, making it difficult to maximize a surface area forheat transfer. As another example, some thermoelectric devices currentlyavailable are substantially thick and not suitable for use in electronicdevices that require more compact thermoelectric devices.

The present disclosure provides thermoelectric elements, devices andsystems, and methods for forming such thermoelectric elements, devicesand systems. Thermoelectric elements and devices of the presentdisclosure can be flexible and able to conform to objects of variousshapes, sizes and configurations, making such elements and devicessuitable for use in various settings, such as consumer and industrialsettings. Thermoelectric elements and devices of the present disclosurecan conform to surfaces to collect waste heat and transform at least afraction of the waste heat to usable energy. In some cases waste heatcan be generated during a chemical, electrical, and/or mechanical energytransformation process.

In an aspect of the present disclosure, a method for forming athermoelectric element having a figure of merit (ZT) that is at leastabout 0.25 comprises (a) providing a reaction space comprising asemiconductor substrate, a working electrode in electrical communicationwith a first surface of the semiconductor substrate, an etching solution(e.g., electrolyte) in contact with a second surface of thesemiconductor substrate, and a counter electrode in the etchingsolution, wherein the first and second surfaces of the semiconductorsubstrate is substantially free of a metallic coating; and (b) using theelectrode and counter electrode to (i) direct electrical current to thesemiconductor substrate at a current density of at least about 0.1mA/cm², and (ii) etch the second surface of the semiconductor substratewith the etching solution to form a pattern of holes in thesemiconductor substrate, thereby forming the thermoelectric elementhaving the ZT that is at least about 0.25, wherein the etch is performedat an electrical potential of at least about 1 volt (V) across thesemiconductor substrate and etching solution, and wherein the etch hasan etch rate that is at least about 1 nanometer (nm) per second at 25°C. In some embodiments, the electrical potential is at least about 1volt (V) across the working electrode, etching solution and counterelectrode.

In some embodiments, the electrical potential is an alternating current(AC) voltage. In some embodiments, the electrical potential is a directcurrent (DC) voltage.

In some embodiments, the working electrode is in contact with the firstsurface. In some embodiments, the working electrode is in ohmic contactwith the first surface. In some embodiments, the semiconductor substrateis part of the working electrode.

In some embodiments, the etch rate is at least about 10 nm per second.In some embodiments, the etch rate is at least about 100 nm per second.In some embodiments, the etch rate is at least about 1000 nm per second.

In some embodiments, the current density is at least about 1 mA/cm². Insome embodiments, the current density is at least about 10 mA/cm². Insome embodiments, the current density is from about 10 mA/cm² to 50mA/cm², 10 mA/cm² to 30 mA/cm², or 10 mA/cm² to 20 mA/cm². In someembodiments, the current density is less than or equal to about 100mA/cm² or 50 mA/cm². In some embodiments, the semiconductor substrate isetched under an alternating current at the current density.

In some embodiments, the working electrode is an anode during theetching. In some embodiments, the method further comprises annealing thesemiconductor substrate subsequent to (b). In some embodiments, themethod further comprises, prior to (b), heating the etching solution toa temperature that is greater than 25° C. In some embodiments, thesemiconductor substrate is etched in the absence of (or without the aidof) a metal catalyst.

In some embodiments, the pattern of holes includes a disordered patternof holes. In some embodiments, the working electrode does not contactthe etching solution.

In some embodiments, the etching solution includes an acid. In someembodiments, the acid is selected from the group consisting of HF, HCl,HBr and HI. In some embodiments, the etching solution includes analcohol additive. In some embodiments, the etch is performed in theabsence of illuminating the semiconductor substrate.

In some embodiments, the ZT is at least 0.5, 0.6, 0.7, 0.8, 0.9, or 1 at25° C. In some embodiments, the semiconductor substrate comprisessilicon.

In another aspect, a method for forming a thermoelectric element havinga figure of merit (ZT) that is at least about 0.25, comprises (a)providing a semiconductor substrate in a reaction space comprising anetching solution (e.g., electrolyte); (b) inducing flow of electricalcurrent to the semiconductor substrate at a current density of at leastabout 0.1 mA/cm²; and (c) using the etching solution to etch thesemiconductor substrate under the current density of at least about 0.1mA/cm² to form a disordered pattern of holes in the semiconductorsubstrate, thereby forming the thermoelectric element having the ZT thatis at least about 0.25, wherein the etching is performed (i) in theabsence of a metal catalyst and (ii) at an electrical potential of atleast about 1 volt (V) across the semiconductor substrate and etchingsolution, and wherein the etching has an etch rate of at least about 1nanometer (nm) per second at 25° C.

In some embodiments, the electrical potential is an alternating current(AC) voltage. In some embodiments, the electrical potential is a directcurrent (DC) voltage.

In some embodiments, the etch rate is at least about 10 nm per second.In some embodiments, the etch rate is at least about 100 nm per second.In some embodiments, the etch rate is at least about 1000 nm per second.

In some embodiments, the current density is at least about 1 mA/cm². Insome embodiments, the current density is at least about 10 mA/cm². Insome embodiments, the current density is from about 10 mA/cm² to 50mA/cm², 10 mA/cm² to 30 mA/cm², or 10 mA/cm² to 20 mA/cm². In someembodiments, the current density is less than or equal to about 100mA/cm² or 50 mA/cm². In some embodiments, the semiconductor substrate isetched under an alternating current at the current density.

In some embodiments, the etching solution includes an acid. In someembodiments, the acid is selected from the group consisting of HF, HCl,HBr and HI. In some embodiments, the etching solution includes analcohol additive. In some embodiments, the etch is performed in theabsence of illuminating the semiconductor substrate.

In some embodiments, the method further comprises annealing thesemiconductor substrate subsequent to (c). In some embodiments, themethod further comprises, prior to (c), heating the etching solution toa temperature that is greater than 25° C. In some embodiments, thesemiconductor substrate comprises silicon.

Another aspect of the present disclosure provides a computer readablemedium comprising machine executable code that, upon execution by one ormore computer processors, implements any of the methods above orelsewhere herein.

Another aspect of the present disclosure provides a computer controlsystem comprising one or more computer processor and memory coupledthereto. The memory comprises machine executable code that, uponexecution by the one or more computer processors, implements any of themethods above or elsewhere herein

In another aspect of the present disclosure, a thermoelectric devicecomprising at least one flexible thermoelectric element including asemiconductor substrate, wherein surfaces of the semiconductor substratehave a metal content less than about 1% as measured by x-rayphotoelectron spectroscopy (XPS), wherein the flexible thermoelectricelement has a figure of merit (ZT) that is at least about 0.25 at 25°C., and wherein the flexible thermoelectric element has a Young'sModulus that is less than or equal to about 1×10⁶ pounds per square inch(psi) at 25° C. as measured by static deflection of the thermoelectricelement.

In some embodiments, the semiconductor substrate has a surface roughnessbetween about 0.1 nanometers (nm) and 50 nm as measured by transmissionelectron microscopy (TEM). In some embodiments, the surface roughness isbetween about 1 nm and 20 nm as measured by TEM. In some embodiments,the surface roughness is between about 1 nm and 10 nm as measured byTEM.

In some embodiments, the metal content is less than or equal to about0.001% as measured by XPS. In some embodiments, the Young's Modulus isless than or equal to about 800,000 psi at 25° C. In some embodiments,the figure of merit is at least about 0.5, 0.6, 0.7, 0.8, 0.9, or 1.

In some embodiments, the semiconductor substrate is chemically dopedn-type or p-type. In some embodiments, the semiconductor substratecomprises silicon.

In some embodiments, the thermoelectric element includes a pattern ofholes. In some embodiments, the pattern of holes is polydisperse. Insome embodiments, the pattern of holes includes a disordered pattern ofholes. In some embodiments, the disordered pattern of holes ispolydisperse.

In some embodiments, the thermoelectric element includes a pattern ofwires. In some embodiments, the pattern of wires is polydisperse. Insome embodiments, the pattern of wires includes a disordered pattern ofwires. In some embodiments, the disordered pattern of wires ispolydisperse.

Another aspect of the present disclosure provides an electronic devicecomprising a flexible thermoelectric element including a semiconductorsubstrate, wherein surfaces of the semiconductor substrate have a metalcontent less than about 1% as measured by x-ray photoelectronspectroscopy (XPS), wherein the flexible thermoelectric element has afigure of merit (ZT) that is at least about 0.25 at 25° C., and whereinthe flexible thermoelectric element bends at an angle of at least about10° relative to a measurement plane at a plastic deformation that isless than 20% as measured by three-point testing.

In some embodiments, the semiconductor substrate has a surface roughnessbetween about 0.1 nanometers (nm) and 50 nm as measured by transmissionelectron microscopy (TEM). In some embodiments, the surface roughness isbetween about 1 nm and 20 nm as measured by TEM. In some embodiments,the surface roughness is between about 1 nm and 10 nm as measured byTEM.

In some embodiments, the metal content is less than or equal to about0.001% as measured by XPS. In some embodiments, the flexiblethermoelectric element bends at an angle of at least about 20° relativeto the measurement plane. In some embodiments, the figure of merit is atleast about 0.5, 0.6, 0.7, 0.8, 0.9, or 1.

In some embodiments, the electronic device is a watch, a health orfitness tracking device, or a waste heat recovery unit. The electronicdevice can be part of a larger system including other electronic devicesand a control module, for example.

In some embodiments, the semiconductor substrate is chemically dopedn-type or p-type. In some embodiments, the semiconductor substratecomprises silicon.

In some embodiments, the electronic device comprises a plurality ofthermoelectric elements. Each of the plurality of thermoelectricelements can be as described above or elsewhere herein. In someembodiments, the plurality of thermoelectric elements are oppositelychemically doped n-type and p-type.

In some embodiments, the thermoelectric element includes a pattern ofholes. In some embodiments, the pattern of holes is polydisperse. Insome embodiments, the pattern of holes includes a disordered pattern ofholes. In some embodiments, the disordered pattern of holes ispolydisperse.

In some embodiments, the thermoelectric element includes a pattern ofwires. In some embodiments, the pattern of wires is polydisperse. Insome embodiments, the pattern of wires includes a disordered pattern ofwires. In some embodiments, the disordered pattern of wires ispolydisperse.

Another aspect of the present disclosure provides a system forgenerating power, comprising a fluid flow channel for directing a fluid;and a thermoelectric device comprising at least one flexiblethermoelectric element adjacent to at least a portion of the fluid flowchannel, wherein the flexible thermoelectric element has a Young'sModulus that is less than or equal to about 1×10⁶ pounds per square inch(psi) at 25° C., wherein the flexible thermoelectric element has a firstsurface that is in thermal communication with the fluid flow channel anda second surface that is in thermal communication with a heat sink, andwherein the thermoelectric device generates power upon the flow of heatfrom the fluid flow channel through the thermoelectric device to theheat sink.

In some embodiments, the thermoelectric device comprises at least twothermoelectric elements that are oppositely chemically doped n-type andp-type. In some embodiments, the Young's Modulus is less than or equalto about 800,000 psi at 25° C.

In some embodiments, the thermoelectric element comprises asemiconductor material. In some embodiments, the semiconductor materialincludes silicon.

In some embodiments, the flexible thermoelectric element substantiallyconforms to a shape of the fluid flow channel. In some embodiments, thefluid flow channel is a pipe. In some embodiments, the fluid flowchannel is cylindrical.

Additional aspects and advantages of the present disclosure will becomereadily apparent to those skilled in this art from the followingdetailed description, wherein only illustrative embodiments of thepresent disclosure are shown and described. As will be realized, thepresent disclosure is capable of other and different embodiments, andits several details are capable of modifications in various obviousrespects, all without departing from the disclosure. Accordingly, thedrawings and description are to be regarded as illustrative in nature,and not as restrictive.

INCORPORATION BY REFERENCE

All publications, patents, and patent applications mentioned in thisspecification are herein incorporated by reference to the same extent asif each individual publication, patent, or patent application wasspecifically and individually indicated to be incorporated by reference.

BRIEF DESCRIPTION OF THE DRAWINGS

The novel features of the invention are set forth with particularity inthe appended claims. A better understanding of the features andadvantages of the present invention will be obtained by reference to thefollowing detailed description that sets forth illustrative embodiments,in which the principles of the invention are utilized, and theaccompanying drawings (also “figure” and “FIG.” herein), of which:

FIG. 1 shows a thermoelectric device having a plurality of elements;

FIG. 2 is a schematic perspective view of a thermoelectric element, inaccordance with an embodiment of the present disclosure;

FIG. 3 is a schematic top view of the thermoelectric element of FIG. 2,in accordance with an embodiment of the present disclosure;

FIG. 4 is a schematic side view of the thermoelectric element of FIGS. 2and 3, in accordance with an embodiment of the present disclosure;

FIG. 5 is a schematic perspective top view of a thermoelectric element,in accordance with an embodiment of the present disclosure;

FIG. 6 is a schematic perspective top view of the thermoelectric elementof FIG. 5, in accordance with an embodiment of the present disclosure;

FIG. 7 is a schematic perspective view of a thermoelectric devicecomprising elements having an array of wires, in accordance with anembodiment of the present disclosure;

FIG. 8 is a schematic perspective view of a thermoelectric devicecomprising elements having an array of holes, in accordance with anembodiment of the present disclosure;

FIG. 9 is a schematic perspective view of a thermoelectric devicecomprising elements having an array of holes that are orientedperpendicularly with respect to the vector V, in accordance with anembodiment of the present disclosure;

FIG. 10 schematically illustrates a method for manufacturing a flexiblethermoelectric device comprising a plurality of thermoelectric elements;

FIG. 11 schematically illustrates a flexible thermoelectric devicehaving a flexible thermoelectric material;

FIG. 12 schematically illustrates a heat recovery system comprising aheat sink and a thermoelectric device;

FIG. 13 schematically illustrates a weldable tube with an integratedthermoelectric device and heat sinks;

FIG. 14A schematically illustrates a flexible heat sink wrapped aroundan object; FIG. 14B is a cross-sectional side view of FIG. 14A;

FIG. 15 schematically illustrates a flexible thermoelectric tape with anintegrated heat sink;

FIG. 16 schematically illustrates an electronic device havingthermoelectric elements in electrical communication with top and bottominterconnects;

FIG. 17A is a schematic perspective side view of a baby monitor; FIG.17B is a schematic angled side view of the baby monitor of FIG. 17A;FIG. 17C is a schematic side view of the baby monitor of FIG. 17A; FIG.17D is a schematic top view of the baby monitor of FIG. 17A;

FIG. 18A is a schematic perspective side view of a pacemaker; FIG. 18Bis a schematic side view of the pacemaker of FIG. 18A; FIG. 18C is aschematic top view of the pacemaker of FIG. 18A;

FIG. 19A is a schematic perspective view of a wearable electronicdevice; FIG. 19B schematically illustrates the wearable electronicdevice of FIG. 19A adjacent to a hand of a user;

FIG. 20 is a schematic perspective view of eyewear;

FIG. 21A is a schematic perspective view of a medical device; FIG. 21Bschematically illustrates the medical device of FIG. 21A mounted on abody of a user;

FIG. 22 schematically illustrates heat recover systems as part of avehicle exhaust system;

FIG. 23A is a schematic perspective side view of a heat recovery andpower generation system installed on a radiator; FIG. 23B is a schematicside view of the heat recovery and power generation system of FIG. 23A;

FIG. 24A is a schematic perspective side view of a heat recovery andpower generation system installed in a heat exchanger; FIG. 24B is aschematic side view of the heat recovery and power generation system ofFIG. 24A;

FIG. 25 shows a computer control system that is programmed or otherwiseconfigured to implement various methods provided herein, such asmanufacturing thermoelectric elements; and

FIG. 26A shows a scanning electron microscopy (SEM) micrograph of athermoelectric element; and FIG. 26B shows an x-ray diffraction (XRD)plot showing bulk and porous silicon in a thermoelectric element.

DETAILED DESCRIPTION

While various embodiments of the invention have been shown and describedherein, it will be obvious to those skilled in the art that suchembodiments are provided by way of example only. Numerous variations,changes, and substitutions may occur to those skilled in the art withoutdeparting from the invention. It should be understood that variousalternatives to the embodiments of the invention described herein may beemployed.

The term “nanostructure,” as used herein, generally refers to structureshaving a first dimension (e.g., width) along a first axis that is lessthan about 1 micrometer (“micron”) in size. Along a second axisorthogonal to the first axis, such nanostructures can have a seconddimension from nanometers or smaller to microns, millimeters or larger.In some cases, the dimension (e.g., width) is less than about 1000nanometers (“nm”), or 500 nm, or 100 nm, or 50 nm, or smaller.Nanostructures can include holes formed in a substrate material. Theholes can form a mesh having an array of holes. In other cases,nanostructure can include rod-like structures, such as wires, cylindersor box-like structure. The rod-like structures can have circular,elliptical, triangular, square, rectangular, pentagonal, hexagonal,heptagonal, octagonal or nonagonal, or other cross-sections.

The term “nanohole,” as used herein, generally refers to a hole, filledor unfilled, having a width or diameter less than or equal to about 1000nanometers (“nm”), or 500 nm, or 100 nm, or 50 nm, or smaller. Ananohole filled with a metallic, semiconductor, or insulating materialcan be referred to as a “nanoinclusion.”

The term “nanowire,” as used herein, generally refers to a wire or otherelongate structure having a width or diameter that is less than or equalto about 1000 nm, or 500 nm, or 100 nm, or 50 nm, or smaller.

The term “n-type,” as used herein, generally refers to a material thatis chemically doped (“doped”) with an n-type dopant. For instance,silicon can be doped n-type using phosphorous or arsenic.

The term “p-type,” as used herein, generally refers to a material thatis doped with an p-type dopant. For instance, silicon can be dopedp-type using boron or aluminum.

The term “metallic,” as used herein, generally refers to a substanceexhibiting metallic properties. A metallic material can include one ormore elemental metals.

The term “monodisperse,” as used herein, generally refers to featureshaving shapes, sizes (e.g., widths, cross-sections, volumes) ordistributions (e.g., nearest neighbor spacing, center-to-center spacing)that are similar to one another. In some examples, monodisperse features(e.g., holes, wires) have shapes or sizes that deviate from one anotherby at most about 20%, 15%, 10%, 5%, 4%, 3%, 2%, 1%, 0.5%, or 0.1%. Insome cases, monodisperse features are substantially monodisperse.

The term “etching material,” as used herein, generally refers to amaterial that facilitates the etching of substrate (e.g., semiconductorsubstrate) adjacent to the etching material. In some examples, anetching material catalyzes the etching of a substrate upon exposure ofthe etching material to an oxidizing agent and a chemical etchant.

The term “etching layer,” as used herein, generally refers to a layerthat comprises an etching material. Examples of etching materialsinclude silver, platinum, chromium, molybdenum, tungsten, osmium,iridium, rhodium, ruthenium, palladium, copper, nickel and other metals(e.g., noble metals), or any combination thereof, or any non-noble metalthat can catalyze the decomposition of a chemical oxidant, such as, forexample, copper, nickel, or combinations thereof.

The term “etch block material,” as used herein, generally refers to amaterial that blocks or otherwise impedes the etching of a substrateadjacent to the etch block material. An etch block material may providea substrate etch rate that is reduced, or in some cases substantiallyreduced, in relation to a substrate etch rate associated with an etchingmaterial. The term “etch block layer,” as used herein, generally refersto a layer that comprises an etch block material. An etch block materialcan have an etch rate that is lower than that of an etching material.

The term “reaction space,” as used herein, generally refers to anyenvironment suitable for the formation of a thermoelectric device or acomponent of the thermoelectric device. A reaction space can be suitablefor the deposition of a material film or thin film adjacent to asubstrate, or the measurement of the physical characteristics of thematerial film or thin film. A reaction space may include a chamber,which may be a chamber in a system having a plurality chambers. Thesystem may include a plurality of fluidically separated (or isolated)chambers. The system may include multiple reactions spaces, with eachreaction space being fluidically separated from another reaction space.A reaction space may be suitable for conducting measurements on asubstrate or a thin film formed adjacent to the substrate.

The term “current density,” as used herein, generally refers to electric(or electrical) current per unit area of cross section, such as thecross section of a substrate. In some examples, current density iselectric current per unit area of a surface of a semiconductorsubstrate.

The term “adjacent” or “adjacent to,” as used herein, includes ‘nextto’, ‘adjoining’, ‘in contact with’, and ‘in proximity to’. In someinstances, adjacent components are separated from one another by one ormore intervening layers. The one or more intervening layers may have athickness less than about 10 micrometers (“microns”), 1 micron, 500nanometers (“nm”), 100 nm, 50 nm, 10 nm, 1 nm, 0.5 nm or less. Forexample, a first layer adjacent to a second layer can be in directcontact with the second layer. As another example, a first layeradjacent to a second layer can be separated from the second layer by atleast a third layer.

Thermoelectric Elements, Devices and Systems

The present disclosure provides thermoelectric elements, devices andsystems that can be employed for use in various applications, such asheating and/or cooling applications, power generation, consumerapplications and industrial applications. In some examples,thermoelectric materials are used in consumer electronic devices (e.g.,smart watches, portable electronic devices, and health/fitness trackingdevices). As another example, a thermoelectric material of the presentdisclosure can be used in an industrial setting, such as at a locationwhere there is heat loss. In such a case, heat can be captured by athermoelectric device and used to generate power.

Thermoelectric devices of the present disclosure can be used to generatepower upon the application of a temperature gradient across suchdevices. Such power can be used to provide electrical energy to varioustypes of devices, such as consumer electronic devices.

Thermoelectric devices of the present disclosure can have variousnon-limiting advantages and benefits. In some cases, thermoelectricdevices can have substantially high aspect ratios, uniformity of holesor wires, and figure-of-merit, ZT, which can be suitable for optimumthermoelectric device performance. With respect to the figure-of-merit,Z can be an indicator of coefficient-of-performance (COP) and theefficiency of a thermoelectric device, and T can be an averagetemperature of the hot and the cold sides of the thermoelectric device.In some embodiments, the figure-of-merit (ZT) of a thermoelectricelement or thermoelectric device is at least about 0.01, 0.02, 0.03,0.04, 0.05, 0.06, 0.07, 0.08, 0.09, 0.1, 0.15, 0.2, 0.25, 0.3, 0.35,0.4, 0.45 0.5, 0.55, 0.6, 0.65, 0.7, 0.75, 0.8, 0.85, 0.9, 0.95, 1.0,1.1, 1.2, 1.3, 1.4, 1.5, 1.6, 1.7, 1.8, 1.9, 2.0, 2.1, 2.2, 2.3, 2.4,2.5, 2.6, 2.7, 2.8, 2.9, or 3.0 at 25° C. In some case, thefigure-of-merit is from about 0.01 to 3, 0.1 to 2.5, 0.5 to 2.0 or 0.5to 1.5 at 25° C.

The figure of merit (ZT) can be a function of temperature. In somecases, ZT increases with temperature. For example, a thermoelectrichaving a ZT of 0.5 at 25° C. can have a greater ZT at 100° C.

Thermoelectric devices of the present disclosure can have electrodeseach comprising an array of nanostructures (e.g., holes or wires). Thearray of nanostructures can include a plurality of holes or elongatestructures, such as wires (e.g., nanowires). The holes or wires can beordered and have uniform sizes and distributions. As an alternative, theholes or wires may not be ordered and may not have a uniformdistribution. In some examples, there is no long range order withrespect to the holes or wires. In some cases, the holes or wires mayintersect each other in random directions. Methods for forming patternedor disordered patterns of nanostructures (e.g., holes or wires) areprovided elsewhere herein.

The present disclosure provides thermoelectric elements that areflexible or substantially flexible. A flexible material can be amaterial that can be conformed to a shape, twisted, or bent withoutexperiencing plastic deformation. This can enable thermoelectricelements to be used in various settings, such as settings in whichcontact area with a heat source or heat sink is important. For example,a flexible thermoelectric element can be brought in efficient contactwith a heat source or heat sink, such as by wrapping the thermoelectricelement around the heat source or heat sink.

A thermoelectric device can include one or more thermoelectric elements.The thermoelectric elements can be flexible. An individualthermoelectric element can include at least one semiconductor substratewhich can be flexible. In some cases, individual semiconductorsubstrates of a thermoelectric element are rigid but substantially thin(e.g., 500 nm to 1 mm or 1 micrometer to 0.5 mm) such that they providea flexible thermoelectric element when disposed adjacent one another.Similarly, individual thermoelectric elements of a thermoelectric devicecan be rigid but substantially thin such that they provide a flexiblethermoelectric device when disposed adjacent one another.

FIG. 1 shows a thermoelectric device 100, in accordance with someembodiments of the present disclosure. The thermoelectric device 100includes n-type 101 and p-type 102 elements disposed between a first setof electrodes 103 and a second set of electrodes 104 of thethermoelectric device 100. The first set of electrodes 103 connectsadjacent n-type 101 and p-type elements, as illustrated.

The electrodes 103 and 104 are in contact with a hot side material 105and a cold side material 106 respectively. In some embodiments, the hotside material 105 and cold side material 106 are electrically insulatingbut thermally conductive. The application of an electrical potential tothe electrodes 103 and 104 leads to the flow of current, which generatesa temperature gradient (AT) across the thermoelectric device 100. Thetemperature gradient (AT) extends from a first temperature (average),T1, at the hot side material 105 to a second temperature (average), T2,at the cold side material 106, where T1>T2. The temperature gradient canbe used for heating and cooling purposes.

The n-type 101 and p-type 102 elements of the thermoelectric device 100can be formed of structures having dimensions from nanometers tomicrometers, such as, e.g., nanostructures. In some situations, thenanostructures are holes or inclusions, which can be provided in anarray of holes (i.e., mesh). In other situations, the nanostructures arerod-like structures, such as nanowires. In some cases, the rod-likestructures are laterally separated from one another.

In some cases, the n-type 101 and/or p-type 102 elements are formed ofan array of wires or holes oriented along the direction of thetemperature gradient. That is, the wires extend from the first set ofelectrodes 103 to the second set of electrodes 104. In other cases, then-type 101 and/or p-type 102 elements are formed of an array of holesoriented along a direction that is angled between about 0° and 90° inrelation to the temperature gradient. In an example, the array of holesis orthogonal to the temperature gradient. The holes or wires, in somecases, have dimensions on the order of nanometers to micrometers. Insome cases, holes can define a nanomesh.

FIG. 2 is a schematic perspective view of a thermoelectric element 200having an array of holes 201 (select holes circled), in accordance withan embodiment of the present disclosure. The array of holes can bereferred to as a “nanomesh” herein. FIGS. 3 and 4 are perspective topand side views of the thermoelectric element 200. The element 200 can bean n-type or p-type element, as described elsewhere herein. The array ofholes 201 includes individual holes 201 a that can have widths fromseveral nanometers or less up to microns, millimeters or more. In someembodiments, the holes have widths (or diameters, if circular) (“d”)between about 1 nm and 500 nm, or 5 nm and 100 nm, or 10 nm and 30 nm.The holes can have lengths (“L”) from about several nanometers or lessup to microns, millimeters or more. In some embodiments, the holes havelengths between about 0.5 microns and 1 centimeter, or 1 micron and 500millimeters, or 10 microns and 1 millimeter.

The holes 201 a are formed in a substrate 200 a. In some cases, thesubstrate 200 a is a solid state material, such as e.g., carbon (e.g.,graphite or graphene), silicon, germanium, gallium arsenide, aluminumgallium arsenide, silicides, silicon germanium, bismuth telluride, leadtelluride, oxides (e.g., SiO_(x), where ‘x’ is a number greater thanzero), gallium nitride and tellurium silver germanium antimony (TAGS)containing alloys. For example, the substrate 200 a can be a Group IVmaterial (e.g., silicon or germanium) or a Group III-V material (e.g.,gallium arsenide). The substrate 200 a may be formed of a semiconductormaterial comprising one or more semiconductors. The semiconductormaterial can be doped n-type or p-type for n-type or p-type elements,respectively.

In some cases, the holes 201 a are filled with a gas, such as He, Ne,Ar, N₂, H₂, CO₂, O₂, or a combination thereof. In other cases, the holes201 a are under vacuum. Alternatively, the holes may be filled (e.g.,partially filled or completely filled) with a semiconductor material, aninsulating (or dielectric) material, or a gas (e.g., He, Ar, H₂, N₂,CO₂).

A first end 202 and second end 203 of the element 200 can be in contactwith a substrate having a semiconductor-containing material, such assilicon or a silicide. The substrate can aid in providing an electricalcontact to an electrode on each end 202 and 203. Alternatively, thesubstrate can be precluded, and the first end 202 and second end 203 canbe in contact with a first electrode (not shown) and a second electrode(not shown), respectively.

In some embodiments, the holes 201 a are substantially monodisperse.Monodisperse holes may have substantially the same size, shape and/ordistribution (e.g., cross-sectional distribution). In other embodiments,the holes 201 a are distributed in domains of holes of various sizes,such that the holes 201 a are not necessarily monodisperse. For example,the holes 201 a may be polydisperse. Polydisperse holes can have shapes,sizes and/or orientations that deviate from one another by at leastabout 0.1%, 0.5%, 1%, 2%, 3%, 4%, 5%, 10%, 15%, 20%, 30%, 40%, or 50%.In some situations, the device 200 includes a first set of holes with afirst diameter and a second set of holes with a second diameter. Thefirst diameter is larger than the second diameter. In other cases, thedevice 200 includes two or more sets of holes with different diameters.

The holes 201 a can have various packing arrangements. In some cases,the holes 201 a, when viewed from the top (see FIG. 3), have a hexagonalclose-packing arrangement. In some embodiments, the holes 201 a in thearray of holes 201 have a center-to-center spacing between about 1 nmand 500 nm, or 5 nm and 100 nm, or 10 nm and 30 nm. In some cases, thecenter-to-center spacing is the same, which may be the case formonodisperse holes 201 a. In other cases, the center-to-center spacingcan be different for groups of holes with various diameters and/orarrangements.

The dimensions (lengths, widths) and packing arrangement of the holes201, and the material and doping configuration (e.g., dopingconcentration) of the element 200 can be selected to effect apredetermined electrical conductivity and thermal conductivity of theelement 200, and a thermoelectric device having the element 200. Forinstance, the diameters and packing configuration of the holes 201 canbe selected to minimize the thermal conductivity, and the dopingconcentration can be selected to maximize the electrical conductivity ofthe element 200.

The doping concentration of the substrate 200 a can be at least about10¹⁸ cm⁻³, 10¹⁹ cm⁻³, 10²⁰ cm⁻³, or 10²¹ cm⁻³. In some examples, thedoping concentration is from about 10¹⁸ to 10²¹ cm⁻³, or 10¹⁹ to 10²⁰cm⁻³. The doping concentration can be selected to provide a resistivitythat is suitable for use as a thermoelectric element. The resistivity ofthe substrate 200 a can be at least about 0.001 ohm-cm, 0.01 ohm-cm, or0.1 ohm-cm, and in some cases less than or equal to about 1 ohm-cm, 0.5ohm-cm, 0.1 ohm-cm. In some examples, the resistivity of the substrate200 a is from about 0.001 ohm-cm to 1 ohm-cm, 0.001 ohm-cm to 0.5ohm-cm, or 0.001 ohm-cm to 0.1 ohm-cm.

The array of holes 201 can have an aspect ratio (e.g., the length of theelement 200 divided by width of an individual hole 201a) of at leastabout 1.5:1, or 2:1, or 5:1, or 10:1, or 20:1, or 50:1, or 100:1, or1000:1, or 5,000:1, or 10,000:1, or 100,000:1, or 1,000,000:1, or10,000,000:1, or 100,000,000:1, or more.

The holes 201 can be ordered and have uniform sizes and distributions.As an alternative, the holes 201 may not be ordered and may not have auniform distribution. For example, the holes 201 can be disordered suchthat there is no long range order for the pattern of holes 201.

In some embodiments, thermoelectric elements can include an array ofwires. The array of wires can include individual wires that are, forexample, rod-like structures.

As an alternative to the array of holes of the element 200, the holesmay not be ordered and may not have a uniform distribution. In someexamples, there is no long range order with respect to the holes. Insome cases, the holes may intersect each other in random directions. Theholes may include intersecting holes, such as secondary holes thatproject from the holes in various directions. The secondary holes mayhave additional secondary holes. The holes may have various sizes andmay be aligned along various directions, which may be random and notuniform.

FIG. 5 is a schematic perspective top view of a thermoelectric element500, in accordance with an embodiment of the present disclosure. FIG. 6is a schematic perspective top view of the thermoelectric element 500.The thermoelectric element 500 may be used with devices, systems andmethods provided herein. The element 500 includes an array of wires 501having individual wires 501 a. In some embodiments, the wires havewidths (or diameters, if circular) (“d”) between about 1 nm and 500 nm,or 5 nm and 100 nm, or 10 nm and 30 nm. The wires can have lengths (“L”)from about several nanometers or less up to microns, millimeters ormore. In some embodiments, the wires have lengths between about 0.5microns and 1 centimeter, or 1 micron and 500 millimeters, or 10 micronsand 1 millimeter.

In some embodiments, the wires 501 a are substantially monodisperse.Monodisperse wires may have substantially the same size, shape and/ordistribution (e.g., cross-sectional distribution). In other embodiments,the wires 501 a are distributed in domains of wires of various sizes,such that the wires 501 a are not necessarily monodisperse. For example,the wires 501 a may be polydisperse. Polydisperse wires can have shapes,sizes and/or orientations that deviate from one another by at leastabout 0.1%, 0.5%, 1%, 2%, 3%, 4%, 5%, 10%, 15%, 20%, 30%, 40%, or 50%.

In some embodiments, the wires 501 a in the array of wires 501 have acenter-to-center spacing between about 1 nm and 500 nm, or 5 nm and 100nm, or 10 nm and 30 nm. In some cases, the center-to-center spacing isthe same, which may be the case for monodisperse wires 501. In othercases, the center-to-center spacing can be different for groups of wireswith various diameters and/or arrangements.

In some embodiments, the wires 501 a are formed of a solid statematerial, such as a semiconductor material, such as, e.g., silicon,germanium, gallium arsenide, aluminum gallium arsenide, silicide alloys,alloys of silicon germanium, bismuth telluride, lead telluride, oxides(e.g., SiO_(x), where ‘x’ is a number greater than zero), galliumnitride and tellurium silver germanium antimony (TAGS) containingalloys. The wires 501 a can be formed of other materials disclosedherein. The wires 501 a can be doped with an n-type dopant or a p-typedopant. The doping concentration of the semiconductor material can be atleast about 10¹⁸ cm⁻³, 10¹⁹ cm⁻³, 10²⁰ cm⁻³, or 10²¹ cm⁻³. In someexamples, the doping concentration is from about 10¹⁸ to 10²¹ cm⁻³, or10¹⁹ to 10²⁰ cm⁻³. The doping concentration of the semiconductormaterial can be selected to provide a resistivity that is suitable foruse as a thermoelectric element. The resistivity of the semiconductormaterial can be at least about 0.001 ohm-cm, 0.01 ohm-cm, or 0.1 ohm-cm,and in some cases less than or equal to about 1 ohm-cm, 0.5 ohm-cm, 0.1ohm-cm. In some examples, the resistivity of the semiconductor materialis from about 0.001 ohm-cm to 1 ohm-cm, 0.001 ohm-cm to 0.5 ohm-cm, or0.001 ohm-cm to 0.1 ohm-cm.

In some embodiments, the wires 501 a are attached to semiconductorsubstrates at a first end 502 and second end 503 of the element 500. Thesemiconductor substrates can have the n-type or p-type dopingconfiguration of the individual wires 501 a. In other embodiments, thewires 501 a at the first end 502 and second end 503 are not attached tosemiconductor substrates, but can be attached to electrodes. Forinstance, a first electrode (not shown) can be in electrical contactwith the first end 502 and a second electrode can be electrical contactwith the second end 503.

With reference to FIG. 6, space 504 between the wires 501 a may befilled with a vacuum or various materials. In some embodiments, thewires are laterally separated from one another by an electricallyinsulating material, such as a silicon dioxide, germanium dioxide,gallium arsenic oxide, spin on glass, and other insulators depositedusing, for example, vapor phase deposition, such as chemical vapordeposition or atomic layer deposition. In other embodiments, the wiresare laterally separated from one another by vacuum or a gas, such as He,Ne, Ar, N₂, H₂, CO₂, O₂, or a combination thereof.

The array of wires 501 can have an aspect ratio—length of the element500 divided by width of an individual wire 501 a—of at least about1.5:1, or 2:1, or 5:1, or 10:1, or 20:1, or 50:1, or 100:1, or 1000:1,or 5,000:1, or 10,000:1, or 100,000:1, or 1,000,000:1, or 10,000,000:1,or 100,000,000:1, or more. In some cases, the length of the element 500and the length of an individual wire 501 a are substantially the same.

Thermoelectric elements provided herein can be incorporated inthermoelectric devices for use in cooling and/or heating and, in somecases, power generation. In some examples, the device 100 may be used asa power generation device. In an example, the device 100 is used forpower generation by providing a temperature gradient across theelectrodes and the thermoelectric elements of the device 100.

As an alternative to the array of wires of the element 500, the wiresmay not be ordered and may not have a uniform distribution. In someexamples, there is no long range order with respect to the wires. Insome cases, the wires may intersect each other in random directions. Thewires may have various sizes and may be aligned along variousdirections, which may be random and not uniform.

FIG. 7 shows a thermoelectric device 700 having n-type elements 701 andp-type elements 702, in accordance with an embodiment of the presentdisclosure. The n-type elements 701 and p-type elements 702 each includean array of wires, such as nanowires. An array of wires can include aplurality of wires. The n-type elements 701 include n-type (or n-doped)wires and the p-type elements 702 include p-type wires. The wires can benanowires or other rod-like structures.

Adjacent n-type elements 701 and p-type elements 702 are electricallyconnected to one another at their ends using electrodes 703 and 704. Thedevice 700 includes a first thermally conductive, electricallyinsulating layer 705 and a second thermally conductive, electricallyinsulating layer 706 at opposite ends of the elements 701 and 702.

The device 700 includes terminals 707 and 708 that are in electricalcommunication with the electrodes 703 and 704. The application of anelectrical potential across the terminals 707 and 708 generates a flowof electrons and holes in the n-type and p-type elements 701 and 702,respectively, which generates a temperature gradient across the elements701 and 702. The first thermally conductive, electrically insulatinglayer 705 is a cold side of the device 700; the second thermallyconductive, electrically insulating layer 706 is a hot side of thedevice 700. The cold side is cooler (i.e., has a lower operatingtemperature) than the hot side.

FIG. 8 shows a thermoelectric device 800 having n-type elements 801 andp-type elements 802, in accordance with an embodiment of the presentdisclosure. The n-type elements 801 and p-type elements 802 are formedin n-type and p-type semiconductor substrates, respectively. Eachsubstrate can include an array of holes, such as nanoholes. The array ofholes can include a plurality of holes. An individual hole can span thelength of an n-type or p-type element. The holes can be monodisperse, inwhich case hole dimensions and center-to-center spacing may besubstantially constant. In some cases, the array of holes includes holeswith center-to-center spacing and hole dimensions (e.g., widths ordiameters) that may be different. In such a case, the holes may not bemonodisperse.

Select n-type elements 801 and p-type elements 802 are electricallyconnected to one another at their ends by electrodes 803 and 804. Thedevice 800 includes a first thermally conductive, electricallyinsulating layer (“first layer”) 805 and a second thermally conductive,electrically insulating layer (“second layer”) 806 at opposite ends ofthe elements 801 and 802.

The device 800 includes terminals 807 and 808 that are in electricalcommunication with the electrodes 803 and 804. The application of anelectrical potential across the terminals 807 and 808 generates the flowof electrons and holes in the n-type and p-type elements 801 and 802,respectively, which generates a temperature gradient across the elements801 and 802. The first thermally conductive, electrically insulatinglayer 805 is a cold side of the device 800; the second thermallyconductive, electrically insulating layer 806 is a hot side of thedevice 800. The cold side is cooler (i.e., has a lower operatingtemperature) than the hot side.

The thermoelectric device 800 has a temperature gradient from the secondthermally conductive, electrically insulating layer 806 to the firstthermally conductive, electrically insulating layer 805. In some cases,the holes are disposed parallel to a vector oriented from the firstlayer 805 to the second layer 806. In other cases, the holes aredisposed at an angle greater than 0° in relation to the vector. Forinstance, the holes can be disposed at an angle of at least about 1°,10°, 20°, 30°, 40°, 50°, 60°, 70°, 80°, or 90° in relation to thevector.

FIG. 9 shows a thermoelectric device 900 having n-type elements 901 andp-type elements 902, with the elements having holes formed in substratesof the n-type and p-type elements. The holes are oriented perpendicularto a vector (“V”) orthogonal to the electrodes 903 and 904 of the device900.

Wires or holes of thermoelectric elements provided herein may be formedin a substrate and oriented substantially anti-parallel to a supportstructure, such as an electrode. In some examples, the wires or holesare oriented at an angle greater than 0°, or 10°, or 20°, or 30°, or40°, or 50°, or 60°, or 70°, or 80°, or 85° in relation to the supportstructure. In an example, the wires or holes are oriented at an angle ofabout 90° in relation to the support structure. The electrode may be anelectrode of a thermoelectric device. In some cases, wires or holes maybe oriented substantially parallel to the electrode.

As an alternative to the devices of FIGS. 7-9, a thermoelectric devicecan have a thermoelectric element with an array of holes or wires withindividual holes or wires that may have different sizes and/ordistributions. An array of holes or wires may not be ordered and may nothave a uniform distribution. In some examples, there is no long rangeorder with respect to the holes or wires. In some cases, the holes orwires may intersect each other in random directions. The holes or wiresmay include intersecting holes or wires, such as secondary holes orwires that project from other holes or wires in various directions. Theholes or wires may have various sizes and may be aligned along variousdirections, which may be random and not uniform. As another alternative,a thermoelectric device can include at least one thermoelectric element(p or n-type) with an order array of holes or wires, and at least onethermoelectric element (p or n-type) with a disordered array of holes orwires. The disordered array of holes or wires may include holes or wiresthat are not ordered and do not have a uniform distribution.

A hole or wire of the disclosure may have a surface roughness that issuitable for optimized thermoelectric device performance. In some cases,the root mean square roughness of a hole or wire is between about 0.1 nmand 50 nm, or 1 nm and 20 nm, or 1 nm and 10 nm. The roughness can bedetermined by transmission electron microscopy (TEM) or other surfaceanalytical technique, such as atomic force microscopy (AFM) or scanningtunneling microscopy (STM). The surface roughness may be characterizedby a surface corrugation.

Methods for Forming Thermoelectric Elements

The present disclosure provides various methods for formingthermoelectric elements. A thermoelectric element can be formed usingelectrochemical etching. In some cases, a thermoelectric element isformed by cathodic or anodic etching, in some cases without the use of acatalyst. A thermoelectric element can be formed without use of ametallic catalysis. A thermoelectric element can be formed withoutproviding a metallic coating on a surface of a substrate to be etched.This can also be performed using purely electrochemical anodic etchingand suitable etch solutions and electrolytes. As an alternative, athermoelectric can be formed using metal catalyzed electrochemicaletching in suitable etch solutions and electrolytes, as described in,for example, PCT/US2012/047021, filed Jul. 17, 2012, PCT/US2013/021900,filed Jan. 17, 2013, PCT/US2013/055462, filed Aug. 16, 2013,PCT/US2013/067346, filed Oct. 29, 2013, each of which is entirelyincorporated herein by reference.

Recognized herein are various benefits to not using catalysts to formthermoelectric elements. In an example, a non-metal catalyzed etch canpreclude the need for metal (or metallic) catalysts, which can providefor fewer processing steps, including cleanup steps to remove the metalcatalysts from the thermoelectric element after etching. This can alsoprovide for reduced manufacturing cost, as metal catalysts can beexpensive. Metal catalysts can include rare and/or expensive metallicmaterials (e.g., gold, silver, platinum, or palladium), and eliminatingthe use of a metallic catalyst can advantageously decrease the cost offorming thermoelectric elements. Additionally, the non-catalyzed processcan be more reproducible and controllable. In some cases, thenon-catalyzed process described herein can be scaled from a relativelysmall production scale of thermoelectric elements to a relatively largerproduction scale of thermoelectric elements.

The present disclosure provides methods for forming thermoelectricmaterials for use in various applications, such as consumer andindustrial applications. In some examples, thermoelectric materials areused in consumer electronic devices (e.g., smart watches, portableelectronic devices, and health/fitness tracking devices). As anotherexample, a thermoelectric material of the present disclosure can be usedin an industrial setting, such as at a location where there is heatloss, which heat can be captured and used to generate power.

The present disclosure provides methods for forming flexible orsubstantially flexible thermoelectric materials. A flexible material canbe a material that bends at an angle of least about 1°, 5°, 10°, 15°,20°, 25°, 30°, 35°, 40°, 45°, 50°, 60°, 70°, 80°, 90°, 100°, 120°, 130°,140°, 150°, 160°, 170°, or 180° relative to a measurement plane withoutexperiencing plastic deformation or breaking. The flexible material canbend under an applied force over a given area of the flexible material(i.e. pressure). Plastic deformation can be measured by, for example,three-point testing (e.g., instron extension) or tensile testing. As analternative or in addition to, the flexible material can be a materialthat bends at an angle of least about 1°, 5°, 10°, 15°, 20°, 25°, 30°,35°, 40°, 45°, 50°, 60°, 70°, 80°, 90°, 100°, 120°, 130°, 140°, 150°,160°, 170°, or 180° relative to a measurement plane at a plasticdeformation that is less than or equal to about 20%, 15%, 10%, 5%, 1%,or 0.1% as measured by three-point testing (e.g., instron extension) ortensile testing. A flexible material can be a substantially pliablematerial. A flexible material can be a material that can conform or moldto a surface. Such materials can be employed for use in varioussettings, such as consumer and industrial settings. Thermoelectricelements formed according to methods herein can be formed into variousshapes and configurations. Such shapes can be changed as desired by auser, such as to conform to a given object. The thermoelectric elementscan have a first shape, and after being formed into a shape orconfiguration the thermoelectric elements can have a second shape. Thethermoelectric elements can be transformed from the second shape to theinitial shape.

In an aspect of the present disclosure, a thermoelectric device (ormaterial) is formed using anodic etching. Anodic etching can beperformed in an electrochemical etch cell that provides electricalconnections to the substrate being etched, one or more reservoirs tohold the etch solutions or electrolytes in contact with the substrate,and access for analytical measurements or monitoring of the etchingprocess. The etch solutions and/or electrolytes can comprise an aqueoussolution. The etch (or etching) solutions and/or electrolytes can be abasic, neutral, or acidic solution. Examples of etching solutionsinclude acids, such as hydrofluoric acid (HF), hydrochloric acid (HCl),hydrogen bromide (HBr), hydrogen iodide (HI), or combinations thereof.The etch solutions and/or electrolytes can be an electrically conductivesolution. In an example, the etch cell includes a top reservoir thatcontains a solution comprising an electrolyte. The top reservoir can besituated adjacent to (e.g., on top of) a substrate to be etched. Thesubstrate to be etched can be substantially free of one or more metallicmaterial, which may be catalytic materials. The substrate to be etchedmay be free of a metallic coating. In some examples, the substrate to beetched has a metal content (e.g., on a surface of the substrate) that isless than about 25%, 20%, 15%, 10%, 5%, 1%, 0.1%, 0.01%, 0.001%,0.0001%, 0.00001%, or 000001%, as measured by x-ray photoelectronspectroscopy (XPS).

An etching solution can include an acid (e.g., HF) or a concentration ofacids (taken as a weight percentage) that is less than or equal to about70%, 60%, 50%, 40%, 30%, 20% or 10% (by weight), in some cases greaterthan or equal to about 1%, 10%, 20%, or 30%. In some examples, theconcentration (by weight) is from about 1% to 60%, or 10% to 50%, or 20%to 45%. The balance of the etching solution can include a solvent (e.g.,water) and an additive, such as an alcohol, carboxylic acid, ketoneand/or aldehyde. In some examples, the additive is an alcohol, such asmethanol, ethanol, isopropanol, or a combination thereof. The additivecan enable the user of lower current densities while formingnanostructures (e.g., holes) with properties that are suitable for usein thermoelectric elements of the present disclosure, such as asubstantially uniform distribution of holes having a disordered pattern.The additive can enable the user of lower current densities whileforming nanostructures (e.g., holes) with properties that are suitablefor use in thermoelectric elements of the present disclosure, such asincreased control of the spacing between two or more holes. The additivecan enable the user of lower current densities while formingnanostructures (e.g., holes) with properties that are suitable for usein thermoelectric elements of the present disclosure, such as spacingbetween two or more holes of at most about 5 nm. The additive can enablethe user of lower current densities while forming nanostructures (e.g.,holes) with properties that are suitable for use in thermoelectricelements of the present disclosure, such as spacing between two or moreholes of at most about 20 nm. The additive can enable the user of lowercurrent densities while forming nanostructures (e.g., holes) withproperties that are suitable for use in thermoelectric elements of thepresent disclosure, such as spacing between two or more holes of at mostabout 100 nm.

Electric current can be sourced to and/or through the substrate using anedge or backside contact, through the solution/electrolyte, and into acounter electrode. The counter electrode can be in electricalcommunication with the top reservoir, in some cases situated in the topreservoir. In some cases, the counter electrode is adjacent or incontact with a topside of the substrate. The body of the etch cell canbe fabricated from materials inert to the etch solution or electrolyte(e.g., PTFE, PFA, polypropylene, HDPE). The edge or backside contact caninclude a metal contact on the substrate, or it can be a liquid contactusing a suitable electrolyte. The counter electrode can include a wireor mesh constructed from a suitable electrode material. The etch cellcan contain mechanical paddles or ultrasonic agitators to maintainsolution motion, or the entire cell may be spun, rotated or shaken. Insome examples, agitating the solution before and/or during etching canprovide for improved etching uniformity. This can enable the electrolyteto be circulated during etching. In another example, the etch cell cancontain one or more recirculating reservoirs and etch chambers, with oneor more solutions/electrolytes.

In an example, an unpatterned substrate is loaded into reaction spaceprovided with up to five or more electrode connections. One of theelectrodes is in ohmic contact with the substrate backside (the workingelectrode) and is isolated from an etchant electrolyte. One of theelectrodes can be in ohmic contact with the substrate backside (theworking electrode) and may not be in contact with an etchantelectrolyte. Another electrode (the counter electrode) can be submergedin the electrolyte but not in direct contact with the substrate, andused to supply current through the electrolyte to the substrate workingelectrode. Another electrode (the reference electrode) is immersed inthe electrolyte and isolated from both the working and counterelectrodes, in some cases using a frit, and used to sense the operatingpotential of the etch cell using a known or predetermined referencestandard. Another two or more electrodes may be placed outside thereaction space in order to set up an external electric field. In somecases, at least two electrodes—a working electrode and a counterelectrode—are required.

The reaction space can be used in a number of ways. In one approach, thereaction space can be used in a two-electrode configuration by passingan anodic current via the substrate backside through a suitableelectrolyte. The electrolyte can be, for example, a liquid mixturecontaining a diluent, such as water, or a fluoride-containing reagent,such as hydrofluoric acid, or an oxidizer, such as hydrogen peroxide.The electrolyte can include surfactants and/or modifying agents. Theworking potential can be sensed during anodization using the counterelectrode in a three-electrode configuration. The anodization can beperformed in the presence of a DC or AC external field using theelectrodes placed outside the reaction space.

In anodic etching, a voltage/current assisted etch of a semiconductorcan result in etching of the semiconductor at a rate dependent on thevoltage/current. The etch rate, etch depth, etch morphology, poredensity, pore structure, internal surface area and surface roughness canbe controlled by the voltage/current, etch solution/electrolytecomposition and other additives, pressure/temperature, front/backsideillumination, and stirring/agitation. They can also be controlled by thecrystal orientation, dopant type, resistivity (doping concentration),and growth process (e.g., float-zone or Czochralski) of thesemiconductor. The resistivity of the semiconductor can be at leastabout 0.001 ohm-cm, 0.01 ohm-cm, or 0.1 ohm-cm, and in some cases lessthan or equal to about 1 ohm-cm, 0.5 ohm-cm, 0.1 ohm-cm. In someexamples, the resistivity of the semiconductor is from about 0.001ohm-cm to 1 ohm-cm, 0.001 ohm-cm to 0.5 ohm-cm, or 0.001 ohm-cm to 0.1ohm-cm.

During etching of a semiconductor substrate using voltage/currentcontrol, a potential or bias (e.g., direct current bias) is applied tothe substrate using an underlying electrode. This can result in thesemiconductor substrate being etched. As a result of anodic etching, thesemiconductor's thermal conductivity can drop significantly. In someexamples, by employing an applied bias, the porosity (mass loss) can becontrolled and tuned and therefore the thermal and electrical propertiescan be controlled. In other examples, by employing a specific etchsolution/electrolyte composition and/or additives the porosity can becontrolled. In yet other examples, by employing any number of variablesalready listed, the porosity can be controlled.

In some cases, the semiconductor substrate is unpatterned and in somecases it is patterned. In an unpatterned etch, the substrate is etcheddirectly in the cell. In a patterned etch, a blocking layer thatprevents etching can first be placed over the semiconductor, and thenremoved in specific locations. This layer may be formed in any mannersuitable (e.g., chemical vapor deposition, spin-coating, oxidation) andthen be removed in a subsequent step in desired locations (e.g., plasmaetching, reactive ion etching, sputtering) using a suitable mask (e.g.,photolithography). Alternatively, a blocking layer can be depositeddirectly (e.g., dip pen lithography, inkjet printing, spray coatingthrough a stencil). Subsequently, a negative replica of the pattern inthe blocking layer is transferred into the substrate during the anodicetch.

The etch can be performed by applying an electrical potential(“potential”) to the semiconductor substrate, in the presence of asuitable etch solution/electrolyte. The potential can be, for example,at least about +0.01 V, +0.02 V, +0.03 V, +0.04 V, +0.05 V, +0.06 V,+0.07 V, +0.08 V, +0.09 V, +0.1 V, +0.2 V, +0.3 V, +0.4 V, +0.5 V, +0.6V, +0.7 V, +0.8 V, +0.9 V, +1.0 V, +2.0 V, +3.0 V, +4.0 V, +5.0 V, +10V, +20 V, +30 V, +40 V, or +50 V relative to a reference, such asground. In some examples, the potential is from about +0.01 V to +20 V,+0.1 V to +10 V, or +0.5 V to +5 V relative to a reference. In someexamples, the potential can range from about +0.01 V to +0.05 V, +0.06 Vto +0.1 V, +0.2 V to +0.5 V, +0.6 V to +1.0 V, +2.0 V to +5.0 V, +10 Vto +20 V, +20V to +30 V, +30V to +40 V, or +40V to +50. In someexamples, the potential is from about +0.5 V to +5 V, or +1 V to +5 V.

The etch can be performed by applying or generating an electricalcurrent (“current”) to or through the semiconductor substrate, in somecases in the presence of a suitable etch solution/electrolyte. Thecurrent can be applied to the substrate upon the application of thepotential to the substrate. The current can have a current density, forexample, of at least about +0.01 milliamps per square centimeter(mA/cm²), +0.1 mA/cm², +0.2 mA/cm², +0.3 mA/cm², +0.4 mA/cm², +0.5mA/cm², +0.6 mA/cm², +0.7 mA/cm², +0.8 mA/cm², +0.9 mA/cm², +1.0 mA/cm²,+2.0 mA/cm², +3.0 mA/cm², +4.0 mA/cm², +5.0 mA/cm², +6.0 mA/cm², +7.0mA/cm², +8.0 mA/cm², +9.0 mA/cm², +10 mA/cm², +20 mA/cm², +30 mA/cm²,+40 mA/cm², +50 mA/cm², +60 mA/cm², +70 mA/cm², +80 mA/cm², +90 mA/cm²,+100 mA/cm², +200 mA/cm², +300 mA/cm², +400 mA/cm², +500 mA/cm², +600mA/cm², +700 mA/cm², +800 mA/cm², +900 mA/cm², +1000 mA/cm². In someexamples, the current density ranges from about 0.01 mA/cm² to 20mA/cm², 0.05 mA/cm² to 10 mA/cm², or 0.01 mA/cm² to 5 mA/cm². In someexamples, the current density ranges from about +0.1 mA/cm² to +0.5mA/cm², +0.6 to +1.0 mA/cm², +1.0 mA/cm² to +5.0 mA/cm², +5.0 mA/cm² to+10 mA/cm², +10 mA/cm² to +20 mA/cm², +20 mA/cm² to +30 mA/cm², +30mA/cm² to +40 mA/cm², +40 mA/cm² to +50 mA/cm², +50 mA/cm² to +60mA/cm², +60 mA/cm² to +70 mA/cm², +70 mA/cm² to +80 mA/cm², +80 mA/cm²to +90 mA/cm², +90 mA/cm² to +100 mA/cm², +10 mA/cm² to +200 mA/cm², +20mA/cm² to +300 mA/cm², +300 mA/cm² to +400 mA/cm², +40 mA/cm² to +500mA/cm², +500 mA/cm² to +600 mA/cm², +600 mA/cm² to +700 mA/cm², +700mA/cm² to +800 mA/cm², +800 mA/cm² to +900 mA/cm², or +900 mA/cm² to+1000 mA/cm². In some examples, the current density is from about 1mA/cm² to 30 mA/cm², 5 mA/cm² to 25 mA/cm², or 10 mA/cm² to 20 mA/cm².Such current densities may be achieved with potential provided herein,such as a potential from about +0.5 V to +5 V, or +1 V to +5 V.

The electrical potential (or voltage) can be measured using a voltmeter,for instance. The voltmeter can be in parallel with the substrate. Forexample, the voltmeter can be measure the electrical potential betweentwo sides of the substrate, or the electrical potential between aworking electrode and counter electrode in solution. The current densitycan be measured using an ammeter. The ammeter can be in series with apower source and the substrate. For example, the ammeter can be coupledto a backside of the substrate.

Thermoelectric elements of the present disclosure can be formed at anetching time that is selected to provide an array of nanostructures(e.g., holes or wires). Etching times can range from 1 second to 2 days,1 minute to 1 day, 1 minute to 12 hours, 10 minutes to 6 hours, or 30minutes to 3 hours. In some examples, the etching time is from 30minutes to 6 hours, or 1 hour to 6 hours. In some cases, etching timescan be at least about 1 second, 10 seconds, 30 seconds, 1 minute, 2minutes, 3 minutes, 4 minutes, 5 minutes, 10 minutes, 30 minutes, 1hour, 2 hours, 3 hours, 4 hours, 5 hours, 6 hours, 12 hours, or 1 day.Such etching times can be used in combination with applied voltageand/or current of the present disclosure.

In some cases, the bias applied to the semiconductor substrate can bechanged during etching to regulate the etch rate, etch depth, etchmorphology, pore density, pore structure, internal surface area andsurface roughness of the semiconductor substrate, including the densityand location of nanostructuring in the semiconductor substrate. Inanother case, the etch solution/electrolyte composition and/or additivescan be changed during etching. In yet other cases, thepressure/temperature or illumination or stirring/agitation can bechanged. Alternatively, more than one of these variables may be changedsimultaneously to obtain the desired etch characteristics.

During the period in which the substrate is etched, the electricalpotential can be constant, varied or pulsed. In an example, theelectrical potential is constant during the etching period. In anotherexample, the electrical potential is pulsed on and off, or from positiveto negative, during the etching period. In another example, theelectrical potential is varied during the etching period, such as variedgradually from a first value to a second value, which second value canbe less than or greater than the first value. The electrical potentialcan then be varied from the second value to the first value, and so on.In yet another example, the bias/current may be oscillated according toa sinusoidal/triangular/arbitrary waveform. In some cases, thebias/current can be pulsed with a frequency of at least about 1 Hz, 10Hz, 1000 Hz, 5000 Hz, 10000 Hz, 50000 Hz, or 100000 Hz.

The bias and/or current can be DC or AC, or a combination of DC and AC.Use of an AC bias and/or current with DC offset can provide control overthe etch rate using the DC bias/current and control over ions using theAC bias/current. The AC bias/current can alternately enhance and retardthe etch rate, or increase/decrease the porosity/surface roughness, ormodify the morphology and structure in a periodic or non-periodicfashion. The amplitude and frequency of the AC bias/current can be usedto tune the etch rate, etch depth, etch morphology, pore density, porestructure, internal surface area and surface roughness.

In some situations, the application of an electrical potential to asemiconductor substrate during etching can provide for a given etchrate. In some examples, the substrate can be etched at a rate of atleast about 0.1 nanometers (nm)/second (s), 0.5 nm/s, 1 nm/s, 2 nm/s, 3nm/s, 4 nm/s, 5 nm/s, 6 nm/s, 7 nm/s, 8 nm/s, 9 nm/s, 10 nm/s, 20 nm/s,30 nm/s, 40 nm/s, 50 nm/s, 60 nm/s, 70 nm/s, 80 nm/s, 90 nm/s, 100 nm/s,200 nm/s, 300 nm/s, 400 nm/s, 500 nm/s, 600 nm/s, 700 nm/s, 800 nm/s,900 nm/s, 1000 nm/s, or 10,000 nm/s at 25° C. In other cases, the etchrate may be increased/decreased with a change in pressure/temperature,solution/electrolyte composition and/or additives, illumination,stirring/agitation.

The porosity of a semiconductor substrate during etching using anapplied potential or current density can provide a substrate with aporosity (mass loss) that can provide a thermoelectric element that issuitable for various applications. In some examples, the porosity is atleast about 0.01%, 0.1%, 1%, 5%, 10%, 20%, 30%, 40%, 50%, or 60%. Theporosity can be from about 0.01% to 99.99%, 0.1% to 60%, or 1% to 50%.

A substrate can have a thickness that is selected to yield athermoelectric element that is suitable for various applications. Thethickness can be at least about 100 nanometers (nm), 500 nm, 1micrometer (micron), 5 microns, 10 microns, 100 microns, 500 microns, 1millimeter (mm), or 10 mm. In some examples, the thickness is from about500 nm to 1 mm, 1 micron to 0.5 mm, or 10 microns to 0.5 mm.

The etch may be performed to completion through the entire thickness ofthe substrate, or it may be stopped at any depth. A complete etch yieldsa self-supporting nanostructured material with no underlying unetchedsubstrate. An incomplete etch yields a layer of nanostructured materialover underlying unetched substrate. The nanostructured layer may have athickness at least about 10 nanometers (nm), 20 nm, 30 nm, 40 nm, 50 nm,60 nm, 70 nm, 80 nm, 90 nm, 100 nm, 200 nm, 300 nm, 400 nm, 500 nm, 600nm, 700 nm, 800 nm, 900 nm, 1 micrometers (μm), 2 μm, 3 μm, 4 μm, 5 μm,6 μm, 7 μm, 8 μm, 9 μm, 10 μm, 20 μm, 30 μm, 40 μm, 50 μm, 60 μm, 70 μm,80 μm, 90 μm, 100 μm, 200 μm, 300 μm, 400 μm, 500 μm, 600 μm, 700 μm,800 μm, 900 μm, 1 millimeters (mm), 2 millimeters (mm), 3 millimeters(mm), 4 millimeters (mm), 5 millimeters (mm), 6 millimeters (mm), 7millimeters (mm), 8 millimeters (mm), 9 millimeters (mm), 10 millimeters(mm) or more.

The nanostructured layer may be left on the substrate, or it may beseparated from the substrate in a number of ways. The layer may bemechanically separated from the substrate (e.g., using a diamond saw,scribing and cleaving, laser cutting, peeling off). Alternatively, thelayer can be separated from the substrate by effecting electropolishingconditions at the etching front at the base of the layer. Theseconditions can be achieved by a change in pressure, change intemperature, change in solution composition, change in electrolytecomposition, use of additives, illumination, stirring, and/or agitation,or by waiting a sufficient duration of time (e.g., more than about 1day). In some cases, a partial or incomplete separation may be desired,such that the layer is still weakly attached to the substrate. This canbe achieved by varying between normal etching conditions andelectropolishing. Complete separation can then be achieved in asubsequent step.

After etching, the material may be chemically modified to yieldfunctionally active or passive surfaces. For example, the material maybe modified to yield chemically passive surfaces, or electronicallypassive surfaces, or biologically passive surfaces, or thermally stablesurfaces, or a combination of the above. This can be accomplished usinga variety of methods, e.g., thermal oxidation, thermal silanation,thermal carbonization, hydrosilylation, Grignard reagents,electrografting. In some cases, one or more of the above methods may beused to obtain a surface with the desired or otherwise predeterminedcombination of properties.

After modification, the voids in the material may also be fully orpartially impregnated with a filling material. For example, the fillingmaterial may be electrically conductive, or thermally insulating, ormechanically strengthening, or a combination of the above. Suitablefilling materials may include one or more of the following groups:insulators, semiconductors, semimetals, metals, polymers, gases, orvacuum. Filling can be accomplished using a variety of methods, e.g.,atomic layer deposition, chemical vapor deposition, deposition fromchemical bath or polymerization bath, electrochemical deposition, dropcasting or spin coating or immersion followed by evaporation of asolvated filling material. In some cases, one or more of the abovemethods may be used to obtain filling materials with the desiredcombination of properties.

After filling, the material may also be sealed with a capping material.For example, the capping material may be impermeable to gases, orliquids, or both. Suitable filling materials may include one or more ofthe following groups: insulators, semiconductors, semimetals, metals orpolymers. Capping can be accomplished using a variety of methods, e.g.,atomic layer deposition, chemical vapor deposition, deposition fromchemical bath or polymerization bath, electrochemical deposition, dropcasting or spin coating or immersion followed by evaporation of asolvated filling material. In some cases, one or more of the abovemethods may be used to obtain capping materials with the desired orpredetermined combination of properties.

After etching, the material can be washed with a suitable rinsingsolution (e.g., water, methanol, ethanol, isopropanol, toluene, hexanesetc.) and dried (e.g., blow drying, evaporative drying, oven/furnacedrying, vacuum drying, critical point drying, or air drying). Therinsing solution can be selected depending on the mode of drying.

After anodic etching, the thermal and electrical properties of thesemiconductor may be further controlled or tuned by coarsening orannealing the semiconductor nanostructure (pore or hole morphology,density, structure, internal surface area and surface roughness) throughthe application of heat and time. Temperatures between about 50° C. and1500° C., or 100° C. and 1300° C. for a time period from about 1 secondto 1 week can be utilized to control the thermal and electricalproperties of the semiconductor. In some cases, the time period is atleast about 1 second, 10 seconds, 30 seconds, 1 minute, 2 minutes, 3minutes, 4 minutes, 5 minutes, 10 minutes, 30 minutes, 1 hour, 2 hours,3 hours, 4 hours, 5 hours, 6 hours, 12 hours, or 1 day. The annealingmay be performed in vacuum (e.g., at a pressure that is from about1×10⁻¹° Torr to <760 Torr) or in the presence of a suitable gas (e.g.,helium, neon, argon, xenon, hydrogen, nitrogen, forming gas, carbonmonoxide, carbon dioxide, oxygen, water vapor, air, methane, ethane,propane, sulfur hexafluoride and mixtures thereof). The gas can be aninert gas. Annealing can be performed on partially or completely etchedsubstrates, completely separated etched layers on unetched substrates,partially separated etched layers on unetched substrates, or unseparatedetched layers on unetched substrates. In some cases, when layers onunetched substrates are annealed, the semiconductor coarsening mayproceed in such a fashion as to separate the layers from the unetchedsubstrate. This can be convenient for effecting layer separation.

Electrical contacts may be deposited on or adjacent to thenanostructured material using standard deposition techniques (e.g.,silk-screening, inkjet deposition, painting, spraying, dip-coating,soldering, metal sputtering, metal evaporation). These may be metalcontacts (e.g., gold, silver, copper, aluminum, indium, gallium,lead-containing solder, lead-free solder or combinations thereof)with/without suitable adhesion layers (e.g., titanium, chromium, nickelor combinations thereof). Alternatively, they may be silicide contacts(e.g., titanium silicide, cobalt silicide, nickel silicide, palladiumsilicide, platinum silicide, tungsten silicide, molybdenum silicideetc.). Barrier layers (e.g., platinum, palladium, tungsten nitride,titanium nitride, molybdenum nitride etc.) may be inserted to preventinter-diffusion between the silicon and the contact, or between contactlayers, or between every layer. In other examples, they may becombinations of both metal and silicide contacts. A silicide contact canbe provided to reduce contact resistance between a metal contact and thesubstrate. Examples of silicides include tungsten silicide, titaniumdisilicide and nickel silicide. A subsequent annealing step may be usedto form the contact and improve its properties. For example annealingcan reduce contact resistance, which can provide an ohmic contact.

After electrical contacts have been formed, the material can beassembled into a thermoelectric device comprising of p- and n-typethermoelectric elements (or legs). A thermoelectric device can includep- and n-legs connected electrically in series, and thermally inparallel with each other. They can be built upon electrically insulatingand thermally conductive rigid plates (e.g., aluminum nitride, aluminumoxide, silicon carbide, silicon nitride etc.) with electricalconnections between the legs provided by metal interconnects (e.g.,copper, aluminum, gold, silver etc.). In another example, thethermoelectric material may be assembled on a flexible insulatingmaterial (e.g., polyimide, polyethylene, polycarbonate etc.). Electricalconnections between the legs are provided via metal interconnectsintegrated on the flexible material. The resulting thermoelectric may bein sheet, roll or tape form. Desired sizes of thermoelectric materialmay be cut out from the sheet, roll or tape and assembled into devices.

Processing conditions (e.g., applied voltages and current densities)provided herein have various unexpected benefits, such as the formationof nanostructures (e.g., holes) having orientations and configurationsthat provide thermoelectric elements and devices of the presentdisclosure with enhanced or otherwise improved properties, such as athermoelectric element with a ZT from about 0.01 to 3, 0.1 to 2.5, 0.5to 2.0 or 0.5 to 1.5 at 25° C. Such processing conditions can providefor the formation of an array nanostructures in a substrate. The arrayof nanostructures can have a disordered pattern. Such processingconditions can provide for the formation of flexible thermoelectricelements or devices.

FIG. 10 schematically illustrates a method for manufacturing a flexiblethermoelectric device comprising a plurality of thermoelectric elements.A p-type or n-type silicon substrate that has been processed using, forexample, a non-catalytic approach described elsewhere herein (e.g.,anodic etching) is coated on both sides with a suitable contactmaterial, such as titanium, nickel, chromium, tungsten, aluminum, gold,platinum, palladium, or any combination thereof. The substrate is thenheated to a temperature of at least about 250° C., 300° C., 350° C.,400° C., 450° C., 500° C., 550° C., 600° C., 650° C., 700° C., 750° C.,800° C., 850° C., 900° C., 950° C., or 1000° C., and cut into multiplepieces using, for example, a diamond cutter, wire saw, or laser cutter.

Next, in a metallization operation, individual pieces of the cutsubstrate are placed on bottom and top tapes having widths of about 30centimeters (cm). The tapes can be formed of a polymeric material, suchas, for example, polyimide, polycarbonate, polyethylene, polypropylene,or copolymers, mixtures and composites of these and other polymers.

Next, the individual pieces are subjected to solder coating to formserial connections to the individual pieces across a given tape. Thetapes are then combined through one or more rollers (two rollers areillustrated). A thermally conductive adhesive can be provided around thetables to help seal the individual pieces between the tapes.

Thermoelectric elements, devices and systems formed according to methodsprovided herein can have various physical characteristics. Theperformance of a thermoelectric device of the disclosure may be relatedto the properties and characteristics of holes and/or wires ofthermoelectric elements. In some cases, optimum device performance maybe achieved for an element having holes or wires, an individual hole orwire having a surface roughness between about 0.1 nm and 50 nm, or 1 nmand 20 nm, or 1 nm and 10 nm, as measured by transmission electronmicroscopy (TEM). In some cases, a thermoelectric element may have aresidual metal content that is less than or equal to about 0.000001%,0.00001%, 0.0001%, 0.001%, 0.01%, 0.1%, 1%, 5%, 10%, 15%, 20%, or 25%,as measured by x-ray photoelectron spectroscopy (XPS).

A thermoelectric element of the present disclosure may have a surfaceroughness that is suitable for optimized thermoelectric deviceperformance. In some cases, the root mean square roughness of a hole orwire is between about 0.1 nm and 50 nm, or 1 nm and 20 nm, or 1 nm and10 nm. The roughness can be determined by transmission electronmicroscopy (TEM) or other surface analytical technique, such as atomicforce microscopy (AFM) or scanning tunneling microscopy (STM). Thesurface roughness may be characterized by a surface corrugation.

Uses of Thermoelectric Elements

Thermoelectric elements, devices and systems of the present disclosurecan be employed for use in various settings or employed for varioususes. Settings can include, without limitation, healthcare, consumer,and industrial settings. Such uses include, without limitation, flexiblethermoelectric tape with flexible heat sinks, wearable electronicdevices powered by body heat, waste heat recovery units for generatingpower (e.g., waste heat recovery unit in a vehicle or chemical plant).

Heat sink can aid in collecting or dissipating heat. A heat sink caninclude one or more heat fins which can be sized and arranged to provideincrease heat transfer area.

FIG. 11 shows a flexible thermoelectric device 1101. The flexiblethermoelectric device 1101 can include thermoelectric elements 1102 in aserial configuration (see, e.g., FIG. 1). The flexible thermoelectricdevice can have a Young's Modulus that is less than or equal to about30×10⁶ pounds per square inch (psi), 20×10⁶ psi, 10×10⁶ psi, 5×10⁶ psi,2×10⁶ psi, 1×10⁶ psi, 900,000 psi, 800,000 psi, 700,000 psi, 600,000psi, 500,000 psi, 400,000, 300,000, or 200,000 psi at 25° C. The Young'sModulus can be measured by static deflection of the thermoelectricelement. The Young's Modulus can be measured by a tensile test.

In some cases, a flexible thermoelectric device can be used with heatsinks and electrical interconnects. The device can be in the shape of atape, film or sheet form. The device can be substantially flat andflexible, which can enable the device to have increased contact surfacearea with a surface.

A heat sink may be any flexible material, which can be sufficientlythermally conductive to provide low internal thermal resistance andsufficiently thin to bend in a flexible manner. In some cases, a heatsink can have a thickness from about 0.1 millimeters (mm) to 100 mm, or1 mm to 10 mm. The heat sink can include thermoelectric elementsprovided herein within or in contact with a matrix or substrate. Thematrix or substrate can be a polymer foil, elastomeric polymer, ceramicfoil, semiconductor foil, insulator foil, insulated metal foil orcombinations thereof. To increase the surface area presented to theenvironment for effective thermal transfer, the matrix or substrate maybe patterned with dimples, corrugations, pins, fins or ribs.

FIG. 12 shows a heat sink 1201 and a thermoelectric device 1202 withthermoelectric material adjacent to the heat sink 1201. Thethermoelectric material can include thermoelectric elements disclosedherein. The thermoelectric device 1202 is adjacent to a mating surface1203, which can be used to mate with an object, such as, for example, apipe or an electronic device (e.g., computer processor). Thethermoelectric material can be flexible and able to conform to the shapeof the molding surface. The heat sink 1201 can include attachmentmembers 1204 that can enable the heat sink 1201 to be secured to theobject.

Heat sinks with integrated or standalone thermoelectric devices can beused with other objects, such as objects with surfaces that can providefor a temperature gradient. For examples, heat sinks can be used withtubes, which may be employed in various settings, such as industrialsettings. FIG. 13 shows a weldable tube 1301 with an integratedthermoelectric device and heat sinks. A cold side heat sink 1302 issituated at an exterior of the tube 1301 and a hot side heat sink 1303is situated at an interior of the tube 1301. The tube 1301 can be formedof a metallic or metal-containing material. A thermoelectric device 1304comprising a thermoelectric material is disposed at an exterior of thetube, between the tube and the cold side heat sink.

FIGS. 14A and 14B show a flexible heat sink 1401 wrapped around anobject 1402, which can be, for example, a pipe carrying a hot or coldfluid. FIG. 14B is a cross-sectional side view of FIG. 14A. The heatsink can include thermoelectric elements in a thermoelectric devicelayer 1403, which can include thermoelectric elements provided herein.The object 1402 can have a hot or cold surface, which can be situatedadjacent to a side of the thermoelectric device layer 1403. An opposingside of the thermoelectric device layer can be situated adjacent to anenvironment that is hotter or colder than the surface, thereby providinga temperature differential. The thermoelectric elements can be inelectrical communication as described herein (see, e.g., FIG. 1) and inelectrical communication with electrical wires 1404 a and 1404 b at anend of the thermoelectric device layer 1403.

As an alternative, the heat sink can be separate from the thermoelectricdevice layer. The thermoelectric device layer can be in the form of atape, which can be wrapped around an object. The heat sink can besubsequently applied to the thermoelectric device layer.

The thermoelectric device may have both sides attached to heat sinks, orhave only one side attached to a heat sink, or have neither sideattached to a heat sink. The thermoelectric device may have both sidescoated with adhesive, or have only one side coated with adhesive, orhave neither side coated with adhesive. The adhesive can permit thethermoelectric device to be securely coupled to an object and/or one ormore heat sinks. The adhesive can be sufficiently thermally conductive.

Heat sink substrates or matrixes may be any flexible electricallyinsulating material, which can be thin enough to present a low thermalresistance. Examples include polymer foil (e.g., polyethylene,polypropylene, polyester, polystyrene, polyimide, etc.); elastomericpolymer foil (e.g., polydimethylsilazane, polyisoprene, natural rubber,etc.); fabric (e.g., conventional cloths, fiberglass mat, etc.);ceramic, semiconductor, or insulator foil (e.g., glass, silicon, siliconcarbide, silicon nitride, aluminum oxide, aluminum nitride, boronnitride, etc.); insulated metal foil (e.g., anodized aluminum ortitanium, coated copper or steel, etc.); or combinations thereof. Thesubstrate can be both flexible and stretchable when an elastomericmaterial is used.

FIG. 15 shows a flexible thermoelectric tape with an integrated heatsink. The tape includes a flexible heat sink 1501 and a thermoelectricmaterial 1502 adjacent to the heat sink. The heat sink 1501 includes apattern of dimples, which can provide for improved surface area for heattransfer. The tape can include electrical wires that are coupled toelectrodes of the thermoelectric material 1502. The wires can besituated at an end of the tape.

The tape can be applied to various objects, such as planar or non-planarobjects. In an example, the tape is wrapped around a pipe. The tape canbe supplied from a roll and applied to an object from the roll.

Thermoelectric elements, devices and systems of the present disclosurecan be used with electrical interconnects. The electrical interconnectsmay be any flexible electrically conductive material, which can besufficiently thin to present low electrical resistance. Examples includemetals and their alloys and intermetallics (e.g., aluminum, titanium,nickel, chromium, nichrome, tantalum, hafnium, niobium, zirconium,vanadium, tungsten, indium, copper, silver, platinum, gold, etc.),silicides (e.g., titanium silicide, nickel silicide, chromium silicide,tantalum silicide, hafnium silicide, zirconium silicide, vanadiumsilicide, tungsten silicide, copper silicide), conductive ceramics(e.g., titanium nitride, tungsten nitride, tantalum nitride, etc.), orcombinations thereof. The thermoelectric elements may be formed offlexible substrates, such as materials that are sufficiently thin to beflexible. Examples of such materials include bismuth telluride, leadtelluride, half-heuslers, skutterudites, silicon, and germanium. In someexamples, the thermoelectric elements are formed of a nanostructuredsemiconductor (e.g., silicon), which can be made sufficiently thin to beflexible. The nanostructure semiconductor can have a thickness that isless than or equal to about 100 micrometer (microns), 10 microns, 1micron, 0.5 microns, or 0.1 microns. FIG. 16 shows an electronic devicehaving thermoelectric elements 1601 that are used with top interconnects1602 and bottom interconnects 1603. The thermoelectric elements 1601 canbe situated between at least a portion of the top interconnects 1602 anda bottom interconnects 1603. The interconnects 1602 and 1603 andthermoelectric elements 1601 can be disposed on a substrate 1604. Theinterconnects 1602 and 1603 can have a linear pattern 1605 or a zigzagpattern 1606.

In some cases, depending on the combination of component materials used,the flexible thermoelectric device may be optimally used at conditionsat room temperature, near room temperature, or at temperaturessubstantially below room temperature, or at temperatures substantiallyabove room temperature. The choice of nanostructured semiconductor forthe thermoelectric elements can permit effective operation of the deviceacross a broad temperature range spanning at least about −273° C. toabove 1000° C.

Additionally, depending on the power rating, the interconnect patternmay be varied. For example, given a fixed device size, the outputcurrent can be maximized if the thermoelectric elements are connected inparallel linear chains. As another example, the output current can behalved and the output voltage doubled, if the thermoelectric elementsare connected in a zigzag pattern (see FIG. 16). Many interconnectpatterns are possible. Additionally, external circuitry or switches maybe used to switch on/off specific interconnection segments, reroute theinterconnection network, or step up/down the output voltage or current.

In some embodiments, thermoelectric elements, devices and systemsprovided herein can be used in or with wearable electronic devices. Suchwearable electronic devices can be powered at least in part by bodyheat. For example, a thermoelectric device can be provided in a shirt orjacket lining, which can help generate power using the temperaturedifference between the body of a user and the external environment. Thiscan be used to directly provide power to an electronic device (e.g.,wearable electronic device or mobile device), or to charge arechargeable battery of the electronic device.

A thermoelectric material can be integrated in an apparatus thatconverts body heat to electricity for purposes of powering electroniccircuits. The apparatus can be integrated with a wearable electronicdevice, including, but not limited to, smart watches, smart glasses,worn or in-ear media players, consumer health monitors (such aspedometers or baby monitors), hearing aids, medical devices (such asheart rate monitors, blood pressure monitors, brain activity (EEG)monitors, cardiac activity (EKG) monitors, pulse oximeters, insulinmonitors, insulin pumps, pacemakers, wearable defibrillators). Theapparatus can be a standalone apparatus that can be used to powerelectronic devices, such as mobile electronic devices, including, butnot limited to, smart phones (e.g., Apple® iPhone) or laptop computers.The apparatus can be integrated into an electronically augmented pieceof clothing or body accessory, including, but not limited to, smartclothing, smart jewelry (e.g., bracelets, bangles, rings, earrings,studs, necklaces, wristbands, or anklets). The apparatus may be used asthe sole source of electrical power, generating at least about 1 μW, 10μW, 100 μW, 1 mW, 10 mW, 20 mW, 30 mW, 40 mW, 50 mW, 100 mW, or 1 W, insome cases from 1 μW to 10 mW. It can also be augmented or supported byanother source (e.g., battery, capacitors, supercapacitors, photovoltaicpanels, kinetic energy, or rechargeable from wall).

In an example, the apparatus includes a heat collector, a heat expeller,and a thermoelectric device sandwiched there between so as to beinterposed in the primary path of heat flow. In another example, theapparatus may be integrated with power management circuitry (e.g., stepup transformers, direct current (DC) to DC converters, trickle chargecircuits, etc.) or power storage (battery, capacitor, supercapacitor,etc.). In yet another example, the apparatus may be further integratedwith sensors, data storage, communication and/or display circuitry, andmicroprocessor systems.

A heat collector can absorb heat from the body of a user and channelheat to the thermoelectric device. It may take any form amenable for itspurpose and can be sufficiently thermally conductive to absorb heat fromthe body and channel heat to the thermoelectric device. In some cases, aheat collector is a slab, plate, ring, or annulus. The heat collectorcan be formed of a thermally conductive metal, ceramic, or plastic. Inan example, the heat collector is a metallic band. In another example,the heat collector may be integrated with a heat pipe. The heatcollector may be held on the body by physical insertion, loose or tightclamping, friction, or adhesives.

In some cases, the heat expeller can remove heat from the thermoelectricdevice and expel heat to the environment. The heat expeller can have anyshape, form or configuration, such as, for example, a slab, plate, ring,or annulus. The heat expeller can be sufficiently thermally conductiveto remove heat from the thermoelectric device and expel it to theenvironment. In some cases, the heat expeller is formed of a thermallyconductive metal, ceramic, or plastic. In an example, the heat expelleris a metallic heat sink. In another example, the heat expeller may beintegrated with a heat pipe.

The thermoelectric device can convert heat into electricity, and may berigid, semi-rigid or flexible. In some cases, use of a flexiblethermoelectric device can simplify manufacturing and assembly of theapparatus. In an example, this may be one or more layers of a flexiblethermoelectric device and attached between the heat collector andexpeller using thermally conductive adhesives, mechanical preforming ormechanical clamping.

In some cases, the apparatus may take the form of a bracelet or ring. Inanother implementation, the apparatus may take the form of spectacleframes. In yet another implementation, the apparatus may take the formof a patch to be applied over a human chest, back or torso usingadhesive or attachment straps. In yet another implementation, theapparatus may take the form of an implantable film, disc or plate. Theapparatus can provide an output power from the thermoelectric device ofat least about 1 microwatts (μW), 10 μW, 100 μW, 1 mW, 10 milliwatts(mW), 20 mW, 30 mW, 40 mW, 50 mW, 100 mW, or 1 watt (W), in some casesfrom 1 μW to 10 mW, at a voltage of at least about 1 mV, 2 mV, 3 mV, 4mV, 5 mV, 10 mV, 20 mV, 30 mV, 40 mV, 50 mV, 100 mV, 200 mV, 300 mV, 400mV, 500 mV, 1 V, 2 V, 3 V, 4 V, 5 V or 10 V, in some cases from about 10mV-10 V. In some situations, a lower voltage can be converted to atleast about 1 V, 2, V, 2.1 V, 2.2 V, 2.3 V, 2.35 V, 2.4 V, 2.45 V, 2.5V, 3 V, 3.1 V, 3.2 V, 3.3 V, 3.4 V, 3.5 V, 3.6 V, 3.7 V, 3.8 V, 3.9 V, 4V, 4.1 V, 4.2 V, 4.3 V, 4.4 V, 4.5 V, or 5.0 V using a DC-DC converterand associated power management circuitry, and is used to power circuitsdirectly or to trickle charge a power storage unit such as a battery. Anauxiliary power supply, such as a battery, can also be included in theapparatus to provide reserve power in times of intermittent bodilycontact, decreased power output or increased power consumption. Theapparatus can also contain a set of sensors, display and communicationcircuits, and microprocessors to measure, store and display information.

FIGS. 17A-17D show various views of a baby monitor. The baby monitor canbe powered at least in part by body heat, such as the body heat of ababy. The baby monitor includes a band or belt 1701 and a buckle orharness piece 1702 that is integrated with heat collectors and heatexpellers, a thermoelectric device with thermoelectric material, powermanagement electronics and energy storage, a sensor, a communicationsinterface (e.g., for wireless communication with another electronicdevice) and a computer processor.

FIGS. 18A-18D s various views of a body heat powered pacemaker system.The system includes a pacemaker 1801, an implantable thermoelectricmodule 1802 comprising a thermoelectric device of the presentdisclosure, and power leads 1803. The thermoelectric module 1802 can bein film, disc or plate form, for example.

FIGS. 19A and 19B schematically illustrate an electronic device that canbe body heat powered and wearable by a user (e.g., as jewelry). Thedevice comprises a control module 1902 having a sensor display,communications interface and computer processor, which can be inelectrical communication with one another. The device 1901 furthercomprises a heat expeller 1903, thermoelectric device 1904 having athermoelectric material, a heat collector 1905, and a power module 1906having power management electronics and an energy storage system. Theenergy storage system can be a battery, such as a rechargeable battery.The thermoelectric device 1904 can be in electrical communication withthe control module 1902. Power to the control module 1902 can be atleast partially provided by the thermoelectric device 1904 eitherdirectly to the control module 1902 or, in some cases, used to chargethe energy storage system in the power module 1906. FIG. 19B shows thedevice 1901 disposed around a hand 1907 of a user.

FIG. 20 shows eyewear 2001 that can be configured to operate on power atleast partially generated from body heat. The eyewear 2001 comprises acontrol module 2002 that includes a sensor, communications interface anda computer processor, which can be in electrical communication with oneanother. The eyewear 2001 further comprises a heat expeller 2003,thermoelectric device 2004, a heat collector 2005, and a power module2006 having power management electronics and an energy storage system.The thermoelectric device 2004 can be in electrical communication withthe control module 2002. Power to the control module 2002 can be atleast partially provided by the thermoelectric device 2004 eitherdirectly to the control module 2002 or, in some cases, used to chargethe energy storage system in the power module 2006, which can thenprovide power to the control module 2002.

The control module 2002 can be configured to present content to theuser, such as on at least one of the glasses 2007 of the eyewear 2001.The content can include electronic communications, such as text messagesand electronic mail, geographic navigation information, network content(e.g., content from the World Wide Web), and documents (e.g., textdocument).

FIGS. 21A and 21B show a medical device 2101 that can be configured tooperate on power at least partially generated from body heat. Themedical device 2101 comprises a control module and power module, asdescribed elsewhere herein. The medical device 2101 further comprises aheat expeller 2102 on one surface and a heat collector 2103 on anopposing surface, and a thermoelectric device 2104 with thermoelectricmaterial between the heat expeller and the heat collector. Thethermoelectric device 2104 can be in electrical communication with thecontrol module and the power module. FIG. 21B shows the medical device2101 disposed adjacent the body 2105 of a user.

In some cases, during use of a device having a thermoelectric device,heat from an object (e.g., body of a user) generates a temperaturegradient (high temperature to low temperature) from a heat collector toa heat expeller. The heat collector collects heat and the heat expellerexpels heat. The temperature gradient can be used to generate powerusing a thermoelectric device between the heat collector and heatexpeller.

Thermoelectric elements, devices and systems provided herein can be usedin a vehicle waste heat recovery, such as in an apparatus that usesthermoelectric materials to convert vehicular waste heat to electricity(or electric power). The apparatus can be integrated with componentscommon to automotive vehicles, including, but not limited to, engineblocks, heat exchangers, radiators, catalytic converters, mufflers,exhaust pipes and various components in the cabin of the vehicle, suchas a heating and/or air conditioning unit, or components common toindustrial facilities, including, but not limited to, turbine blocks,engine blocks, exchangers, radiators, reaction chambers, chimneys andexhaust. The apparatus may be used as the sole source of electricalpower to the vehicle or an electrical component of the vehicle (e.g.,radio, heating or air conditioning unit, or control system), generatingat least about 1 W, 2 W, 3 W, 4 W, 5 W, 6 W, 7 W, 8 W, 9 W, 10 W, 20 W,30 W, 40 W, 50 W, 60 W, 70 W, 80 W, 90 W, 100 W, 200 W, 300 W, 400 W,500 W, 600 W, 700 W, 800 W, 900 W, 1000 W, or 5000 W of power, in somecases from about 100 W to 1000 W of power. Power from the apparatus canbe augmented or supported by another power source. For example, in thecontext of automotive vehicles, power can be augmented or supported bypower from a battery, alternator, regenerative braking, or a vehicularrecharge station. As another example, in the context of industrial orcommercial facilities, power can be augmented or supported by power fromone or more of batteries, generators, the power grid, turbine blocks,engine blocks, heat exchangers, radiators, reaction chambers, chimneysand exhaust, and/or a renewable energy source, such as one or more ofsolar power, wind power, wave power, and geothermal power.

Flexible thermoelectric devices can be wrapped around pipes throughwhich hot fluid can be flowed. The wrapped pipes may also be furtherintegrated with heat sinks to increase thermal transfer. The hot fluidmay be hot exhaust, hot water, hot oil, hot air etc. Over the wrappedpipes, a cool fluid can be flowed. The cool fluid may be cool exhaust,cool water, cool oil, cool air etc. The wrapped pipes may be enclosedwithin a housing through which the coolant is flowed if the coolantfluid is to be isolated from the ambient environment. They may beexposed to the environment if the coolant fluid is ambient air or water.

In an implementation, an apparatus for power generation from heat is apower generating pipe wrapping. Hot fluid (such as hot exhaust) ispassed through a pipe wrapped with thermoelectric devices. The hot sideof the thermoelectric device may be physically or chemically bonded tothe external surface of the tube to improve thermal transfer. The coldside of the thermoelectric device may be physically or chemically bondedwith heat sinks to improve thermal transfer. A cool fluid (e.g., air orwater) can be forced over the wrapped pipes to extract heat from the hotfluid. The thermoelectric devices interspersed in the path of heat flowcan convert heat to electricity, providing an output power at leastabout 1 W, 2 W, 3 W, 4 W, 5 W, 6 W, 7 W, 8 W, 9 W, 10 W, 20 W, 30 W, 40W, 50 W, 60 W, 70 W, 80 W, 90 W, 100 W, 200 W, 300 W, 400 W, 500 W, 600W, 700 W, 800 W, 900 W, 1000 W, or 5000 W, in some cases from about 100W to 1000 W. If desired, a lower voltage can be converted to at leastabout 1 V, 2, V, 2.1 V, 2.2 V, 2.3 V, 2.35 V, 2.4 V, 2.45 V, 2.5 V, 3 V,3.1 V, 3.2 V, 3.3 V, 3.4 V, 3.5 V, 3.6 V, 3.7 V, 3.8 V, 3.9 V, 4 V, 4.1V, 4.2 V, 4.3 V, 4.4 V, 4.5 V, or 5.0 V using a DC-DC converter andassociated power management circuitry, and is used to power circuitsdirectly or to trickle charge a power storage unit such as a battery.

In another implementation, an apparatus for power generation from heatis a power generating exhaust pipe. Hot fluid (such as hot exhaust gas)can be passed through a pipe wrapped with thermoelectric devices. Thehot side of the thermoelectric device may be physically or chemicallybonded to the external surface of the tube to improve thermal transfer.The cold side of the thermoelectric device may be physically orchemically bonded with heat sinks to improve thermal transfer. Tofurther increase the surface area of the pipe and improve thermaltransfer, the pipe internal surface may be molded with dimples,corrugations, pins, fins or ribs. The pipe may be made from a materialthat is readily weldable, extrudable, machinable or formable, such as,for example, steel, aluminum etc. A cool fluid (e.g., air or water) canbe forced over the wrapped pipes to extract heat from the hot fluid. Thethermoelectric devices interspersed in the path of heat flow can convertheat to electricity, providing an output power at least about 1 W, 2 W,3 W, 4 W, 5 W, 6 W, 7 W, 8 W, 9 W, 10 W, 20 W, 30 W, 40 W, 50 W, 60 W,70 W, 80 W, 90 W, 100 W, 200 W, 300 W, 400 W, 500 W, 600 W, 700 W, 800W, 900 W, 1000 W, or 5000 W, in some cases from about 100 W to 1000 W.If desired, a lower voltage can be converted to at least about 1 V, 2,V, 2.1 V, 2.2 V, 2.3 V, 2.35 V, 2.4 V, 2.45 V, 2.5 V, 3 V, 3.1 V, 3.2 V,3.3 V, 3.4 V, 3.5 V, 3.6 V, 3.7 V, 3.8 V, 3.9 V, 4 V, 4.1 V, 4.2 V, 4.3V, 4.4 V, 4.5 V, or 5.0 V using a DC-DC converter and associated powermanagement circuitry, and is used to power circuits directly or totrickle charge a power storage unit such as a battery.

In yet another implementation, an apparatus for power generation fromheat is a discrete power generating unit to be installed on an exhaustpipe or on any hot surface. A hot surface can be placed in contact withthe apparatus containing thermoelectric devices. A mating face can beprovided, which can be attached in close physical contact to a hotsurface using any suitable technique (e.g., bolted, strapped, welded,brazed, or soldered). The hot side of the thermoelectric device may bephysically or chemically bonded to the opposite side of the mating faceto improve thermal transfer. The cold side of the thermoelectric devicemay be physically or chemically bonded with heat sinks to improvethermal transfer. A cool fluid (such as air) can be forced over the unitto extract heat from the hot surface. The thermoelectric devicesinterspersed in the path of heat flow can convert heat to electricity,providing an output power at least about 1 W, 2 W, 3 W, 4 W, 5 W, 6 W, 7W, 8 W, 9 W, 10 W, 20 W, 30 W, 40 W, 50 W, 60 W, 70 W, 80 W, 90 W, 100W, 200 W, 300 W, 400 W, 500 W, 600 W, 700 W, 800 W, 900 W, 1000 W, or5000 W, in some cases from about 100 W to 1000 W. If desired, a lowervoltage can be converted to at least about 1 V, 2, V, 2.1 V, 2.2 V, 2.3V, 2.35 V, 2.4 V, 2.45 V, 2.5 V, 3 V, 3.1 V, 3.2 V, 3.3 V, 3.4 V, 3.5 V,3.6 V, 3.7 V, 3.8 V, 3.9 V, 4 V, 4.1 V, 4.2 V, 4.3 V, 4.4 V, 4.5 V, or5.0 V using a DC-DC converter and associated power management circuitry,and is used to power circuits directly or to trickle charge a powerstorage unit such as a battery.

FIG. 22 schematically illustrates thermoelectric power recovery fromvehicle exhaust. Apparatuses for heat recovery can be installed atvarious locations of an exhaust pipe 2201, such as clamped around acatalytic converter 2202, welded in an in-line fashion 2203, and/orwrapped around 2204 at least a portion of the exhaust pipe 2201.

During use, exhaust gas is directed from a manifold 2205 through thepipe 2201 to a muffler 2206. Waste heat in the exhaust gas can be usedto generate power using one or more apparatuses for heat recovery, whichcan generate power from waste heat.

In another implementation, an apparatus for power generation from heatis a power generating radiator unit. Hot fluid (such as hot water orsteam, hot oil) can be passed through a series of pipes wrapped withthermoelectric devices. The hot side of the thermoelectric device may bephysically or chemically bonded to the external surface of the tube toimprove thermal transfer. The cold side of the thermoelectric device maybe physically or chemically bonded with heat sinks to improve thermaltransfer. A cool fluid (such as air) can be forced over the wrappedpipes to extract heat from the hot fluid. The thermoelectric devicesinterspersed in the path of heat flow can convert heat to electricity,providing an output power at least about 1 W, 2 W, 3 W, 4 W, 5 W, 6 W, 7W, 8 W, 9 W, 10 W, 20 W, 30 W, 40 W, 50 W, 60 W, 70 W, 80 W, 90 W, 100W, 200 W, 300 W, 400 W, 500 W, 600 W, 700 W, 800 W, 900 W, 1000 W, or5000 W, in some cases from about 100 W to 1000 W. If desired, a lowervoltage can be converted to at least about 1 V, 2, V, 2.1 V, 2.2 V, 2.3V, 2.35 V, 2.4 V, 2.45 V, 2.5 V, 3 V, 3.1 V, 3.2 V, 3.3 V, 3.4 V, 3.5 V,3.6 V, 3.7 V, 3.8 V, 3.9 V, 4 V, 4.1 V, 4.2 V, 4.3 V, 4.4 V, 4.5 V, or5.0 V using a DC-DC converter and associated power management circuitry,and is used to power circuits directly or to trickle charge a powerstorage unit such as a battery.

FIGS. 23A and 23B show an apparatus for heat recovery and powergeneration installed in a radiator 2301, which comprises a hot fluidinlet 2302 in fluid communication with a hot fluid outlet 2303, inaddition to cooling fans 2304. The radiator 2301 can be part of avehicle. Hot pipes of the radiator are at least partially wrapped by aheat recovery apparatus 2305 comprising a flexible thermoelectric devicewith flexible heat sinks. The flexible thermoelectric device can includethermoelectric elements disclosed herein.

During use, a hot fluid is directed from the hot fluid inlet 2302 to thehot fluid outlet 2303. Waste heat in the fluid can be used to generatepower using the apparatus 2305 for heat recovery, which can generatepower from the waste heat.

In another implementation, an apparatus for power generation from heatis a power generating exchanger unit. Hot fluid (e.g., hot water orsteam, or hot oil) can be passed through a series of pipes wrapped withthermoelectric devices. The hot side of the thermoelectric device may bephysically or chemically bonded to the external surface of the tube toimprove thermal transfer. The cold side of the thermoelectric device maybe physically or chemically bonded with heat sinks to improve thermaltransfer. A cool fluid (e.g., cool water or cool oil) can be pumped overthe wrapped pipes to extract heat from the hot fluid. The thermoelectricdevices interspersed in the path of heat flow can convert heat toelectricity, providing an output power at least about 1 W, 2 W, 3 W, 4W, 5 W, 6 W, 7 W, 8 W, 9 W, 10 W, 20 W, 30 W, 40 W, 50 W, 60 W, 70 W, 80W, 90 W, 100 W, 200 W, 300 W, 400 W, 500 W, 600 W, 700 W, 800 W, 900 W,1000 W, or 5000 W, in some cases from about 100 W to 1000 W. If desired,a lower voltage can be converted to at least about 1 V, 2, V, 2.1 V, 2.2V, 2.3 V, 2.35 V, 2.4 V, 2.45 V, 2.5 V, 3 V, 3.1 V, 3.2 V, 3.3 V, 3.4 V,3.5 V, 3.6 V, 3.7 V, 3.8 V, 3.9 V, 4 V, 4.1 V, 4.2 V, 4.3 V, 4.4 V, 4.5V, or 5.0 V using a DC-DC converter and associated power managementcircuitry, and is used to power circuits directly or to trickle charge apower storage unit such as a battery.

FIGS. 24A and 24B show an apparatus for heat recovery and powergeneration installed in a heat exchanger 2401, which comprises a hotfluid inlet 2402 in fluid communication with a hot fluid outlet 2403 anda cold fluid inlet 2404 in fluid communication with a cold fluid outlet2405. The heat exchanger 2401 further includes baffles 2406 to directcold fluid flow, and hot pipes 2407 wrapped with a flexiblethermoelectric device.

During use, a hot fluid (e.g., steam) is directed from the hot fluidinlet 2402 to the hot fluid outlet 2403 and a cold fluid (e.g., liquidwater) is directed from the cold fluid inlet 2404 to the cold fluidoutlet 2405. The hot fluid flow through the hot pipes 2407 anddissipates heat to the cold fluid being directed from the fold fluidinlet 2404 to the cold fluid outlet 2405. Waste heat in the fluid can beused to generate power using the flexible thermoelectric device wrappedaround the hot pipes 2407.

Computer Control Systems

The present disclosure provides computer control systems that areprogrammed or otherwise configured to implement various methods of thedisclosure, such as manufacturing a thermoelectric element. FIG. 25shows a computer system (also “system” herein) 2501 programmed orotherwise configured to facilitate the formation of thermoelectricdevices of the disclosure. The system 2501 can be programmed orotherwise configured to implement methods described herein. The system2501 includes a central processing unit (CPU, also “processor” and“computer processor” herein) 2505, which can be a single core or multicore processor, or a plurality of processors for parallel processing.The system 2501 also includes memory 2510 (e.g., random-access memory,read-only memory, flash memory), electronic storage unit 2515 (e.g.,hard disk), communications interface 2520 (e.g., network adapter) forcommunicating with one or more other systems, and peripheral devices2525, such as cache, other memory, data storage and/or electronicdisplay adapters. The memory 2510, storage unit 2515, interface 2520 andperipheral devices 2525 are in communication with the CPU 2505 through acommunications bus (solid lines), such as a motherboard. The storageunit 2515 can be a data storage unit (or data repository) for storingdata. The system 2501 is operatively coupled to a computer network(“network”) 2530 with the aid of the communications interface 2520. Thenetwork 2530 can be the Internet, an internet and/or extranet, or anintranet and/or extranet that is in communication with the Internet. Thenetwork 2530 in some cases is a telecommunication and/or data network.The network 2530 can include one or more computer servers, which canenable distributed computing, such as cloud computing. The network 2530in some cases, with the aid of the system 2501, can implement apeer-to-peer network, which may enable devices coupled to the system2501 to behave as a client or a server.

The system 2501 is in communication with a processing system 2535 forforming thermoelectric elements and devices of the disclosure. Theprocessing system 2535 can be configured to implement various operationsto form thermoelectric devices provided herein, such as formingthermoelectric elements and forming thermoelectric devices (e.g.,thermoelectric tape) from the thermoelectric elements. The processingsystem 2535 can be in communication with the system 2501 through thenetwork 2530, or by direct (e.g., wired, wireless) connection. In anexample, the processing system 2535 is an electrochemical etchingsystem. In another example, the processing system 2535 is a dry box.

The processing system 2535 can include a reaction space for forming athermoelectric element from the substrate 2540. The reaction space canbe filled with an electrolyte and include electrodes for etching (e.g.,cathodic or anodic etching).

Methods as described herein can be implemented by way of machine (orcomputer processor) executable code (or software) stored on anelectronic storage location of the system 2501, such as, for example, onthe memory 2510 or electronic storage unit 2515. During use, the codecan be executed by the processor 2505. In some examples, the code can beretrieved from the storage unit 2515 and stored on the memory 2510 forready access by the processor 2505. In some situations, the electronicstorage unit 2515 can be precluded, and machine-executable instructionsare stored on memory 2510.

The code can be pre-compiled and configured for use with a machine havea processor adapted to execute the code, or can be compiled duringruntime. The code can be supplied in a programming language that can beselected to enable the code to execute in a pre-compiled or as-compiledfashion.

Aspects of the systems and methods provided herein, such as the system2501, can be embodied in programming. Various aspects of the technologymay be thought of as “products” or “articles of manufacture” typicallyin the form of machine (or processor) executable code and/or associateddata that is carried on or embodied in a type of machine readablemedium. Machine-executable code can be stored on an electronic storageunit, such memory (e.g., read-only memory, random-access memory, flashmemory) or a hard disk. “Storage” type media can include any or all ofthe tangible memory of the computers, processors or the like, orassociated modules thereof, such as various semiconductor memories, tapedrives, disk drives and the like, which may provide non-transitorystorage at any time for the software programming. All or portions of thesoftware may at times be communicated through the Internet or variousother telecommunication networks. Such communications, for example, mayenable loading of the software from one computer or processor intoanother, for example, from a management server or host computer into thecomputer platform of an application server. Thus, another type of mediathat may bear the software elements includes optical, electrical andelectromagnetic waves, such as used across physical interfaces betweenlocal devices, through wired and optical landline networks and overvarious air-links. The physical elements that carry such waves, such aswired or wireless links, optical links or the like, also may beconsidered as media bearing the software. As used herein, unlessrestricted to non-transitory, tangible “storage” media, terms such ascomputer or machine “readable medium” refer to any medium thatparticipates in providing instructions to a processor for execution.

Hence, a machine readable medium, such as computer-executable code, maytake many forms, including but not limited to, a tangible storagemedium, a carrier wave medium or physical transmission medium.Non-volatile storage media include, for example, optical or magneticdisks, such as any of the storage devices in any computer(s) or thelike, such as may be used to implement the databases, etc. shown in thedrawings. Volatile storage media include dynamic memory, such as mainmemory of such a computer platform. Tangible transmission media includecoaxial cables; copper wire and fiber optics, including the wires thatcomprise a bus within a computer system. Carrier-wave transmission mediamay take the form of electric or electromagnetic signals, or acoustic orlight waves such as those generated during radio frequency (RF) andinfrared (IR) data communications. Common forms of computer-readablemedia therefore include for example: a floppy disk, a flexible disk,hard disk, magnetic tape, any other magnetic medium, a CD-ROM, DVD orDVD-ROM, any other optical medium, punch cards paper tape, any otherphysical storage medium with patterns of holes, a RAM, a ROM, a PROM andEPROM, a FLASH-EPROM, any other memory chip or cartridge, a carrier wavetransporting data or instructions, cables or links transporting such acarrier wave, or any other medium from which a computer may readprogramming code and/or data. Many of these forms of computer readablemedia may be involved in carrying one or more sequences of one or moreinstructions to a processor for execution.

Methods described herein can be automated with the aid of computersystems having storage locations with machine-executable codeimplementing the methods provided herein, and a processor for executingthe machine-executable code.

Example 1

A thermoelectric element is formed by providing a semiconductorsubstrate in a reaction chamber having an etching solution comprisinghydrofluoric acid at a concentration from about 10% to 50% (by weight)HF. The semiconductor substrate has a dopant concentration such that thesemiconductor substrate has a resistivity from about 0.001 ohm-cm to 0.1ohm-cm. The etching solution is at a temperature of about 25° C. Aworking electrode is brought in contact with a backside of the substrateand a counter electrode is submerged in the etching solution facing afront side of the substrate. The counter electrode is not in contactwith the substrate. Next, a power source is used to force a currentdensity from about 10 mA/cm² to 20 mA/cm², which yields an electricalpotential of about 1 V between the working electrode and the counterelectrode. The applied electrical potential and flow of electricalcurrent is maintained for a time period of about 1 hour. This forms adisordered pattern of holes in the substrate.

Example 2

A thermoelectric element is formed according to the method described inExample 1. FIGS. 26A and 26B show an SEM micrograph and XRD spectrum,respectively, of the thermoelectric element. The SEM micrograph isobtained under the following conditions: 5 kilovolts (kV) and a workingdistance of 5 millimeters. The SEM micrograph shows a disordered patternof holes in silicon. The XRD spectrum shows two peaks. The taller peak(left) is of porous silicon and the smaller peak (right) is of bulksilicon.

Devices, systems and methods provided herein may be combined with ormodified by other devices, systems and methods, such as devices, systemsand/or methods described in U.S. Pat. No. 7,309,830 to Zhang et al.,U.S. Patent Publication No. 2006/0032526 to Fukutani et al. U.S. PatentPublication No. 2009/0020148 to Boukai et al., U.S. patent applicationSer. No. 13/550,424 to Boukai et al., PCT/US2012/047021, filed Jul. 17,2012, PCT/US2013/021900, filed Jan. 17, 2013, PCT/US2013/055462, filedAug. 25, 2013, and PCT/US2013/067346, filed Oct. 29, 2013, each of whichis entirely incorporated herein by reference.

While preferred embodiments of the present invention have been shown anddescribed herein, it will be obvious to those skilled in the art thatsuch embodiments are provided by way of example only. It is not intendedthat the invention be limited by the specific examples provided withinthe specification. While the invention has been described with referenceto the aforementioned specification, the descriptions and illustrationsof the embodiments herein are not meant to be construed in a limitingsense. Numerous variations, changes, and substitutions will now occur tothose skilled in the art without departing from the invention.Furthermore, it shall be understood that all aspects of the inventionare not limited to the specific depictions, configurations or relativeproportions set forth herein which depend upon a variety of conditionsand variables. It should be understood that various alternatives to theembodiments of the invention described herein may be employed inpracticing the invention. It is therefore contemplated that theinvention shall also cover any such alternatives, modifications,variations or equivalents. It is intended that the following claimsdefine the scope of the invention and that methods and structures withinthe scope of these claims and their equivalents be covered thereby.

What is claimed is:
 1. A method for forming a thermoelectric elementhaving a figure of merit (ZT) that is at least about 0.25, comprising:(a) providing a reaction space comprising a semiconductor substrate, aworking electrode in electrical communication with a first surface ofsaid semiconductor substrate, an etching solution in contact with asecond surface of said semiconductor substrate, and a counter electrodein said etching solution, wherein said first and second surfaces of saidsemiconductor substrate is substantially free of a metallic coating; and(b) using said electrode and counter electrode to (i) direct electricalcurrent to said semiconductor substrate at a current density of at leastabout 0.1 mA/cm², and (ii) etch said second surface of saidsemiconductor substrate with said etching solution to form a pattern ofholes in said semiconductor substrate, thereby forming saidthermoelectric element having said ZT that is at least about 0.25,wherein said etch is performed at an electrical potential of at leastabout 1 volt (V) across said semiconductor substrate and said etchingsolution, and wherein said etch has an etch rate that is at least about1 nanometer (nm) per second at 25° C.
 2. The method of claim 1, whereinsaid etch rate is at least about 100 nm per second.
 3. The method ofclaim 1, wherein said current density is at least about 10 mA/cm². 4.The method of claim 3, wherein said current density is less than orequal to about 50 mA/cm².
 5. The method of claim 1, further comprising,prior to (b), heating said etching solution to a temperature that isgreater than 25° C.
 6. The method of claim 1, wherein said semiconductorsubstrate is etched in the absence of a metal catalyst.
 7. The method ofclaim 1, wherein said pattern of holes includes a disordered pattern ofholes.
 8. The method of claim 1, wherein said etching solution includesan acid selected from the group consisting of HF, HCl, HBr and HI. 9.The method of claim 1, wherein said etching solution includes an alcoholadditive.
 10. The method of claim 1, wherein said etch is performed inthe absence of illuminating said semiconductor substrate.
 11. A methodfor forming a thermoelectric element having a figure of merit (ZT) thatis at least about 0.25, comprising: (a) providing a semiconductorsubstrate in a reaction space comprising an etching solution; (b)inducing flow of electrical current to said semiconductor substrate at acurrent density of at least about 0.1 mA/cm²; and (c) using said etchingsolution to etch said semiconductor substrate under said current densityof at least about 0.1 mA/cm² to form a disordered pattern of holes insaid semiconductor substrate, thereby forming said thermoelectricelement having said ZT that is at least about 0.25, wherein said etchingis performed (i) in the absence of a metal catalyst and (ii) at anelectrical potential of at least about 1 volt (V) across saidsemiconductor substrate and said etching solution, and wherein saidetching has an etch rate of at least about 1 nanometer (nm) per secondat 25° C.
 12. The method of claim 11, wherein said current density is atleast about 10 mA/cm².
 13. The method of claim 12, wherein said currentdensity is less than or equal to about 50 mA/cm².
 14. The method ofclaim 11, wherein said semiconductor substrate is etched under analternating current at said current density.
 15. The method of claim 11,wherein said etching solution includes an acid selected from the groupconsisting of HF, HCl, HBr and HI.
 16. The method of claim 11, furthercomprising, prior to (c), heating said etching solution to a temperaturethat is greater than 25° C.
 17. A thermoelectric device comprising atleast one flexible thermoelectric element including a semiconductorsubstrate, wherein surfaces of said semiconductor substrate have a metalcontent less than about 1% as measured by x-ray photoelectronspectroscopy (XPS), wherein said flexible thermoelectric element has afigure of merit (ZT) that is at least about 0.25 at 25° C., and whereinsaid flexible thermoelectric element has a Young's Modulus that is lessthan or equal to about 1×10⁶ pounds per square inch (psi) at 25° C. asmeasured by static deflection of said thermoelectric element.
 18. Thethermoelectric device of claim 17, wherein said semiconductor substratehas a surface roughness between about 0.1 nanometers (nm) and 50 nm asmeasured by transmission electron microscopy (TEM).
 19. Thethermoelectric device of claim 18, wherein said surface roughness isbetween about 1 nm and 20 nm as measured by TEM.
 20. The thermoelectricdevice of claim 17, wherein said metal content is less than or equal toabout 0.001% as measured by XPS.
 21. The thermoelectric device of claim17, wherein said figure of merit is at least about 0.5.
 22. Thethermoelectric device of claim 21, wherein said figure of merit is atleast about 0.8.
 23. The thermoelectric device of claim 17, wherein saidsemiconductor substrate comprises silicon.
 24. The thermoelectric deviceof claim 17, wherein said thermoelectric element includes a disorderedpattern of holes.
 25. The thermoelectric device of claim 24, whereinsaid disordered pattern of holes is polydisperse.
 26. An electronicdevice comprising a flexible thermoelectric element including asemiconductor substrate, wherein surfaces of said semiconductorsubstrate have a metal content less than about 1% as measured by x-rayphotoelectron spectroscopy (XPS), wherein said flexible thermoelectricelement has a figure of merit (ZT) that is at least about 0.25 at 25°C., and wherein said flexible thermoelectric element bends at an angleof at least about 10° relative to a measurement plane at a plasticdeformation that is less than 20% as measured by three-point testing.27. The electronic device of claim 26, wherein said flexiblethermoelectric element bends at an angle of at least about 20° relativeto said measurement plane.
 28. The electronic device of claim 26,wherein said metal content is less than or equal to about 0.001% asmeasured by XPS.
 29. The electronic device of claim 26, wherein saidelectronic device is a watch, a health or fitness tracking device, or awaste heat recovery unit.
 30. The electronic device of claim 26, whereinsaid thermoelectric element includes a disordered pattern of holes.